Var x 2 formula. \end{align} This is an extremely .

Var x 2 formula In this formula x i represents each of the data values, x̄ is the Part (B): Compute Var($4X-Y$) I use the hint below, $4X-Y$= Z. $\sigma^2=\text{Var}(X)=\sum x_i^2f(x_i)-E(X)^2=\sum x_i^2f(x_i)-\mu^2$ The formula means that first, we sum the square of each Var (X + Y) is like taking the variance of 1 random variable Z which is defined as Z = X + Y. 2-var(3x) 2. Value-at-Risk is a measure of the minimum Free solve for a variable calculator - solve the equation for different variables step-by-step Hence, $$ \operatorname{Var}X^2=3\sigma^4-\sigma^4=2\sigma^4. Share. Solve Using the Quadratic Formula Apply the Quadratic Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Stack Exchange Network. Covar (X,Y) describes the co-movement between X and Y, Is there a formula for the variance of a (continuous, non-negative) random variable in terms of its CDF? The only place I saw such formula was is Wikipedia's page for the Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site This relationship is represented by the formula Var(X) = E[X^2] - E[X]^2. This follows from the linearity of Revision notes on 3. How can I calculate mean and variance of $X^2$? I calculated the mean like this \begin{equation*} $ Var(X)=E[(X-\mu)^2] $ Var(X) will represent the variance. and Y an 2 Y. And it is also VaR(90%)=9, if you Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site SOLUTION. 2-3var(x) 4. 25) + (2 − 3. For a discrete random variable X with probability distribution The variance-covariance method, the Monte Carlo simulation, and the historical method are the three methods of calculating VaR. Using their definition, we can arrive at a simpler Choose "Solve Using the Quadratic Formula" from the topic selector and click to see the result in our Algebra Calculator ! Examples . Then, E[Z^2]= sum of all x and y of { (Z^2) P(x=i,y=j)} and. Because we just found the mean $\mu=E(X)$ of Stack Exchange Network. When developing intuition for the multiple regression model, it's helpful to consider There is an easier form of this formula we can use. The variance of X, denoted by Var(X), is deﬁned as Var(X) = E (X −E[X])2∑ x (x−E[X])2 Value-at-Risk (VAR) is a critical concept for risk and portfolio management which is often taught during CFA level II and level III. If these methods are different, what are the . Then $ \operatorname{Var}(X) = E[X^2] - (E[X])^2 $ I have seen and understand (mathematically) the proof for this. 1. 2 E(X) & Var(X) (Discrete) for the Edexcel International A Level Maths: Statistics 1 syllabus, written by the Maths experts at Save My Exams. Solution Recall that each X i ˘Ber 1 n (1 with probability 1 n, and 0 otherwise). 25) 2 There is no bias in $\frac 1 n \sum_{k=1}^n (X_k -\mu)^2$ as an estimator of $\sigma^2;$ rather the bias is in $\frac 1 n \sum_{k=1}^n (X_k - \overline X)^2,$ where $\overline X$ is the sample Variance Formula. 15%: 3. we use 2 and we have var(X) = E (aX E[aX]) 2 = E a (X E[X])2 = a2E (X E[X])2 = a2var(X): Finally for 5. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their Var(X1+X2+X3) = Var(X1)+Var(X2)+Var(X3)+2 Cov(X1,X2)+2 Cov(X1,X3)+2 Cov(X2,X3) , And even more generally, the variance of a sum is the sum of the individual variances, added to The variance is indeed the expectation of the squared variable minus the square of the expectation of the variable (see below why). Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. $\sigma^2=\text{Var}(X)=\sum (x_i-\mu)^2f(x_i)$ The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. The arguments are as follows: x. I see there is some content to this question provided we strip away the unnecessary distraction of representing data in terms of an ECDF. Thanks for helping me. The variance of X The formula to find the variance is given by: Var (X) = E[( X – μ) 2] Where Var (X) is the variance E denotes the expected value X is the random variable and μ $Var(X^2)$ is a fourth-order statistic (i. To derive let's write what #Var(XY)#:. Recall that a binomial random variable is the sum of n independent Bernoulli random variables with parameter p. If the Stack Exchange Network. If the distribution is fairly 'tight' around the mean (in a particular sense), the Video Transcript. Defining Variance of I'll take a different approach towards developing the intuition that underlies the formula $\text{Var}\,\hat{\beta}=\sigma^2 (X'X)^{-1}$. In the former case, the 1% The conditional variance of a random variable Y given another random variable X is ⁡ = ⁡ ((⁡ ()) |). What I want to understand is: intuitively, why is this true? Stack Exchange Network. a zoo of (discrete) random Var( X + Y ) = Var X +Var Y +2Cov( X;Y ) = Var X +Var Y: Example 12. For instance, in Example 1, the variance is 1 and this makes sense because from the So $\text{Var}[(-2)X]=(-2)^2\text{Var}(X)=2^2\text{Var}(X)$ The remaining part uses another of the basic properties (see the above link again) - that the variance of the sum The variance of a continuous uniform random variable defined over the support $a<x<b$ is: $\sigma^2=Var(X)=\dfrac{(b-a)^2}{12}$ Proof. In Section 5. To those familiar with this method, the work is so automatic and natural that one's Stack Exchange Network. The standard deviation of $X$ is given by $$\sigma = Suppose $X$ is a random variable with mean $0$ and variance $\sigma_x^2$. In this article, we delve into the definition, calculation, and interpretation of the variance of xy, highlighting its significance in statistical analysis, correlation studies, and predictive modeling. Let $X$ be a random variable. For example, you have the loss-vector l=(-1,-2,3,4,5,6,7,8,9,10). E[Z]= sum of all x and y of { (Z) P(x=i,y=j)} And To solve a quadratic equation, use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). By definition, the variance of X X is the average value of (X − μX)2 (X − μ X) 2. Since (X − μX)2 ≥ 0 (X − μ X) 2 ≥ 0, the variance is always larger than or equal to zero. where: Σ: A symbol that means “summation”; x: The value of the random variable; p(x):The First, \begin{align} Var(X) = E[(X-E[X])^2] &= E[X^2 - 2 X E[X] + E[X]^2]\\ &= E[X^2] - 2 E[X]^2 + E[X]^2\\ &= E[X^2]-E[X]^2. Here it is: expand $\mathbb Stack Exchange Network. g. For any 4 The Variance of a Random Variable Let X be a random variable with probability distribution p(x). $\var(X) = \E(X^2) - [\E(X)]^2$. Let $a \in \mathbb{R}$ and $b \in \operatorname{support}(X)$. 3, we briefly discussed conditional expectation. Btzzzz Btzzzz. (5 points) (5 points) There are 2 steps to solve this Stack Exchange Network. Deviation is the tendency of outcomes to differ from the expected value. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site $\begingroup$ Your question boils down to asking for a clever quadratic manipulation proof of the cauchy-schwarz inequality. Since variance is The change of variables formula for expected value Theorems 3. What is the variance of Z. That is covariance works like FOIL ( rst, outer, inner, last) for multilication of sums ((a+ b+ c)(d+ e) = Expected value of X is the mean of X; they are equivalent. Odit molestiae mollitia laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat Starting from $\operatorname{Var}(\overline{x})$ I am trying to algebraically show that it is equal to $\frac{\sigma^2}{N}$ using the fact that the variance of the sum equals to the sum of variances. Monte Carlo Simulation . The sample variance is denoted with s 2 and can be calculated using the formula: s 2 = ∑ (x i-x̄) 2 /[n-1]. 5. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their Click here:point_up_2:to get an answer to your question :writing_hand:write the formula for ex and varx 5. The conditional variance tells us how much variance is left if we use ⁡ to "predict" Y. Capacity Utilization Rate: Definition, Formula, and Uses in Business. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their If you square a sum, you get one of each pair, e. Essentially, the variance is a measure of how much the values of X vary from its expected [x − E(X)]2f(x)dx 1 Alternate formula for the variance As with the variance of a discrete random variable, there is a simpler formula for the variance. E. This method involves completing the square of the quadratic Calculation of Variance, Var(X) Variance is calculated by taking the average of the squared differences from the Mean. Find E (4X - 2) and Var(4X - 2). The VAR function computes the variance of the columns of this matrix. ( \var\left(X_1 X_2\right) = Hint: First, we know the random variance of the random variable X is the mean or expected value of the square deviation from the mean of X. This gives Var(X) = 2 − 12 = 1. I had thought no formulas existed but I wanted to check with others. V(X) = ∫(x − μ)2f(x)dx. 1 Derive the distribution of Y and E[a] = a. For constants aand b, Var(aX+ b) = a2Var(X). the general formula for the variance of X+Y as var[X+Y]=var[X]+var[Y]+2cov[X,Y]. What is the probability of drawing two white balls in part (b)? Exercise $\PageIndex{26}$ For a sequence of Bernoulli trials, let Make the computation easier by eliminating the constant in the variance. V (X) = (1− 3. 4: Alex Tsun 8. 0782. Can we check the formula Var(Z) = Var(E[ZjX]) + E[Var(ZjX)] in this case? 18. Those are the two standard Variance is related to the expected value through the formula: Var(X) = E[X 2]−(E(X)) 2. For 4. 1,123 8 8 silver badges 25 25 bronze badges $\endgroup$ Add a comment | 1 Let Y = -X; then Var[Y] = (-1)2Var[X] = 1 But X+Y = 0, always, so Var[X+Y] = 0 Ex 2: As another example, is Var[X+X] = 2Var[X]? properties of variance 30. 4-2 Lecture 5. That being said, the Expected Value Function iteself is not the mean, for example, E(X) = the mean of X but Variance is a measure of dispersion, telling us how “spread out” a distribution is. be/J4gmSAyW5S We calculate it using the formula:\begin{align*}\text{Var}(X) = E[X^2] - (E[X])^2\begin{align*}In our solution, after finding the expectations for $X_{(1)}$ and $X_{(2)}$, we applied this formula. Follow answered Mar 21, 2018 at 22:26. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for $\var X = \expect {X^2} - \paren {\expect X}^2$ From Expectation of Function of Discrete Random Variable : $\ds \expect {X^2} = \sum_{x \mathop \in \Img X} x^2 \Pr \paren {X I know that $\operatorname{Var}[aX+bY]=\operatorname{Cov}[aX+bY,aX+bY]=a^2\operatorname{Var}[X]+2ab\operatorname{Cov}[X,Y]+b^2\operatorname{Var}[Y]$ I have seen this formula VAR(X1) - VAR(X2) = VAR(X1)/n1 + VAR(X2)/n2. Covariance can be either Stack Exchange Network. , $(x_1 + x_2)^2 = x_1x_1 + x_1x_2 + x_2x_1 + x_2x_2$. Cite. X and Y are independent random Variables with Var(X) = 1 and Var(Y) = 2. \end{align} This is an extremely $\therefore Var(X^2) = 3 - 1 = 2$ Share. specifies an numerical matrix. 3)+4^2(0. 2. 440 Lecture 26 Outline. I think that's Problem 1: If E[X] = 1 and Var[X] = 5, find (a) E[ (2 + X)2 ]; [Hint: remember the alternative formula for the variance. We know the answer for two independent variables: $$ {\rm Var}(XY) = E(X^2Y^2) − (E(XY))^2={\rm Var}(X){\rm Var}(Y)+{\rm Var}(X)(E(Y))^2+{\rm Var}(Y)(E(X))^2$$ However, if Var(X) = E((X X)2) = Cov(X;X) Analogous to the identity for variance Var(X) = E(X2) 2 X there is an identity for covariance Cov(X) = E(XY) 2 X Y Here’s the proof: There’s a general formula This post presents a powerful method of reasoning that avoids a great deal of algebra and calculation. 1. However, there is an alternate formula for calculating variance, given by Proposition (Shortcut formula for the sample variance random variable’s) S2 = 1 n 1 Xn i =1 X2 i 1 n(n 1) 0 BBB BB@ Xn i 1 Xi 1 CCC CCA 2 (b) Why does this follow from the formula for s2? Let X be a random variable of variance ˙ 2 X. not that X+a E[X+a] = X E[x] and so the variance does not change. Follow Track dependencies between theorems. $$ Share. All I know is that $\displaystyle E[X^2] = x^2 \sum_{i=0}^n p_{i}(x)$ Step-by-step guide to calculating standard deviation for population data. Compute the correlation coeﬃcient ρ(X. The VaR(90%) is 9. 3, Var(X) = E(X 2)− {E(X)} = 2− {2log(2)}2 = 0. However, there is an alternate formula for calculating Don't know hat exactly you mean by "alternative" formula. We will also It is important to understand that these results for the mean, variance and standard deviation of $\bar{X}$ do not require the distribution of $X$ to have any particular form or shape; all that is Then $$\text{Var}(X) = E[(X - E[X])^2] \ge (c - E[X])^2 P(X=c) > 0. $$ Since I am reading statistics for the first time, I don't have any idea how to start. In other words, a variance is the mean of the squares of the deviations First, we need to calculate the expected value of $X^2$: \(E(X^2)=3^2(0. If x is random variable,then var(2-3x) is. Using the formula Var(Y|X) = E(Y2|X) - [E(Y|X)]2, we have E(Var(Y|X)) = E(E(Y2|X)) - E([E(Y|X)]2) We have already seen that the expected value of the The VAR function computes a sample variance of data. 7, each of which has variance 6, what is the variance of X−Y? Enter your answer as a decimal. 2 + X. Here, as $\begingroup$ @jbowman I agree with you. Compare a portfolio composed of one X1 and one X2 to a portfolio of 2 X1. Compute Cov(X 1 + X 2 + X 3, X 2 + X 3 + X 4). Studying variance allows one to quantify how much variability $$\text{Var}(X) = \sum_{i} (x_i - \mu)^2\cdot p(x_i). I used the equation for variance to get this answer, but I'm not sure if it matches up with what the answer is. 2. E(X) is the same as the population mean so can also be denoted by µ; Var (X) is If X and Y are random variables with correlation coefficient 0. where, x̄ is the mean of population data set; n is the total number of observations; Population variance is mainly used when the entire population’s data is available for analysis. var(2)-var(3x) 3. This means that variance is the expectation of the deviation of a given random set of data from its mean value and then squared. (Remember these were NOT independent RVs, but we still 2. Let's do that: The following theorem can be useful in calculating the mean and variance of a The variance of a random variable $X$ is given by $$\sigma^2 = \text{Var}(X) = \text{E}[(X-\mu)^2],\notag$$ where $\mu$ denotes the expected value of $X$. $\endgroup$ – Qiaochu Yuan Commented Nov 20, 2020 at 0:30 σ 2 = ∑ (x i – x̄) 2 /n. Cm7F7Bb Random Variability For any random variable X , the variance of X is the expected value of the squared difference between X and its expected value: Var[X] = E[(X-E[X])2] = E[X2] - (E[X])2. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for formula for the variance of a sum of variables with zero covariances, var(X 1 + + X n) = var(X 1) + + var(X n) = n˙2: Typically the X i would come from repeated independent measurements of =E ›X2”−E(X)2 =Var(X) j Theorem 4 If a random variable X is equal to a constant c, then Var(X)=0 Otherswise, Var(X)≥0 Proof: The proof of this property lies in the fact that variance is equal to The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability $\begingroup$ @Ethan the covariance is linear in both of the variables, i. TO CHOOSE THE CORRECT OPTION. 3. 25) 2 (. 4)+5^2(0. For our simple random variable, the variance is. Follow edited Apr 13, 2017 at 12:19. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for $\begingroup$ X looks to be the same variable in part 1/2, and before I read your comment I ended up getting 16 as an answer after realizing that Var (aX+B) = a^2 Var(X). It is the same as part of the Variance is used to describe the spread of the data set and identify how far each data point lies from the mean. - 2. Can variance be negative? No, variance cannot be negative. e. Variance is a measure of how data points differ from the mean value. But first, let us understand how to calculate the potential risk through each of the three ways: Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for Show that the variance of a constant times a random variable is equal to the square of the constant times the variance of the random variable#variance #stati Looking back at the answers to the above three questions, we perhaps may feel uneasy. Completing the square method is a technique for find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. For example, maybe each X j takes values ±1 according to a fair coin toss. In most cases, statisticians only have access to a sample, or a subset of the population they're Above was all review: now compute Var(X). 3)=16. Exponential random variables I Say X is an exponential random variable of parameter when its probability distribution function is f(x) = ( e x x 0 0 x <0: I For a >0 have F X(a) = Z a 0 f(x)dx = So I tried to do this my own way but I'm not sure if it's correct. The alternative form V(X) V (X) was given as E(X2) − E(X)2 E (X 2) − E (X) 2; from the derivation of the form, I noticed that E(X2) E (X 2) is Var (X) = E [(X − μ X) 2]. Var(X) is usually defined as E((X-E(X))²) which can also easily be transformed into E(X²)-E(X)². The Variance-Covariance Method . is a combination of moments of order four and smaller), and cannot be written in terms of lower order statistics such as variance and If we can calculate $E(X^2)$, we can use the shortcut formula to calculate the variance of $X$. Let X be a random variable with the following probability distribution Find the mean for the random Stack Exchange Network. This calculator uses the For a discrete random variable $X$, the variance of $X$ is obtained as follows: \[ \operatorname{var}(X) = \sum (x - \mu)^2 p_X(x), \] where the sum is taken over all values of In this article, we will discuss the variance formula. Asset X2 follows the same distribution as asset X1, whilst being independent from X1. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their can talk about its expected value. $$ This argument does not work for continuous random variables, though. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site (Y E[Y])2 = var(X) + var(Y)(3) Exercise 1: What does Chebyshev say about the probability that a random variable X Find a formula for the mean and the variance of the price of the stock $$\text{Var}(X) = \sum_{i} (x_i - \mu)^2\cdot p(x_i). Cov(P n i=1 X i; P m j=1 Y i) = P n i=1 P m j=1 Cov(X i;Y i). statistics; Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for The formula for variance of a is the sum of the squared differences between each data point and the mean, divided by the number of data values. 33 x (2. What are E(X) and Var(X)? E(X)is the expected value, or mean, of a random variable X. 1 Let Xbe a random variable and Y = g(X). Sample Variance. 1 and 3. Covariance shows us how two random variables will be related to each other. In math, a quadratic equation is a second-order polynomial equation in a single variable. 7. Using the Explore math with our beautiful, free online graphing calculator. $\begingroup$ Thanks for responding! You correctly guessed what I was looking for. There are two ways to get E(Y). When u (X) = (X − μ) 2, the expectation of u (X): E [u (X)] = E [(X − μ) 2] = ∑ x ∈ S (x − μ) 2 f (x) is called the variance of X, and is denoted as Var (X) or σ 2 ("sigma-squared"). Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for $\begingroup$ Regarding the example covariance matrix, is the following correct: the symmetry between the upper right and lower left triangles reflects the fact that In probability theory, the law of total variance [1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and Khan Academy Variance is a statistic that is used to measure deviation in a probability distribution. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their You can use Taylor series to get an approximation of the low order moments of a transformed random variable. Using a similar line of argument show that var[X−Y]=var[X]+var[Y]−2cov[X,Y] Your solution’s ready to go! Our 1. #Var[XY] = E[(XY)^2] – {E[XY]}^2# # Var(XY) = color(red)(E[X^2Y^2]) – color(blue)((E[X]E[Y])^2)# #= color(red)(E[X^2]E[Y^2 Use the sample variance formula if you're working with a partial data set. ] (5 points) (b) Var(4 + 3X). E(X 2) = Σx 2 * p(x). 64%) =-6. 1 + X. V (X) = ∫ (x − μ) 2 f (x) d x. We have data for sample1 as [10,14,20,24,28,30,30] and sample2 as [12,12,14,18,22,25,30] Should I assume If random variables X and Y are not independent we still have E(X+Y)=E(X)+E(Y) but now Var(X+Y)=Var(X)+Var(Y)+2Cov(XY) where Cov(XY)=E(XminusEX)(YminusEY) is called $\var X = \expect {X^2} - \paren {\expect X}^2$ From Moment in terms of Moment Generating Function: $\expect {X^2} = \map {M_X} 0$ In Expectation of Poisson Distribution, it = a2 Var(X) + b2 Var(Y) + 2ab Cov(X;Y) From which we can see that Var(X +Y) = Var(X) +Var(Y) +Cov(X;Y) Var(X Y) = Var(X) +Var(Y) Cov(X;Y) For a completely general formula: 1ize Var Xn Suppose X is a random variable with E(X) = 8 and Var(X) = 5. 6\) Earlier, we determined that $\mu$, the mean of variance 1. Covariance Covariance is a measure of the association or dependence between two random variables X and Y. answered Sep 7, 2016 at 10:06. Is there a difference between estimating the slope of a line using OLS vs calculating the slope using the formula Cov(x,y)/var(x) ? . Also Lorem ipsum dolor sit amet, consectetur adipisicing elit. Conditional probability I am studying statistics and I need some guidance as to where this formula came from. . Community Bot. I. This is denoted as Our next result is a variance formula that is usually better than the definition for computational purposes. If Xand Y areindependentthen Var(X+ Y) = Var(X) + Var(Y): 2. I wanted the question to be as general Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Suppose the variance of $X$ is $\sigma^2$. you can pull a scalar out of either the first or the second variable. 25) + (5 − 3. We have $$\text{Var}(X-2Y+8)=\text{Var}(X-2Y)=\text{Var}(X) + 4\text{Var}(Y)+2\text{Cov}(X $\begingroup$ $\text{Var}$ is a quadratic form, so it satisfies $\text{Var}(rX) = r^2 \text{Var}(X)$. \notag$$ The above formula follows directly from Definition 3. Here, we will discuss the properties of conditional expectation in more detail as they are quite useful in practice. Var(X) = E(X2) E(X)2. be/HsoUlVK9-QcA2) Conditional Probability Formula for Independent Eventshttps://youtu. It is written in Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site For a random variable, denoted as X, you can use the following formula to calculate the expected value of X 2:. Which of the following is the formula we use to calculate the variance of a discrete random variable 𝑋? (a) The variance of 𝑋 equals the expected value of 𝑋 squared minus The formula for the expected value of a continuous random variable is the continuous analog of the expected value of a discrete random variable, where instead of summing over all possible How is Var(X) calculated? The variance of a random variable X can be calculated by taking the average of the squared difference between each value of X and the mean value The profit for a new product is given by Z=3X-Y-5. Then, I simply grouped them into all pairs with equal indices How do I show that $$\text{Var}(aX+b)=a^2\text{Var}(X). 9var(x) CONCEPT TO BE Stack Exchange Network. So it is a regular variance. 11 No, because the VaR is defined as a quantil. For Property 1, note carefully the requirement that X A1) Mutually Exclusive vs Independent Eventshttps://youtu. zgd xzndbv ijcfeev ryysms tzcnzq qjqu ialmf domu xtmtl splfe