Question

Let X,Y be discrete random variables. Let µX and \sigma 2 X be the mean and variance of X; µY and \sigma 2 Y be the mean and variance of Y. Let \sigma XY be the covariance between X and Y. Let a,b,c be constants. Show the following: (HINT: Use the definitions first.) 1 (1) E[a +bX] = a+bE[X] (2) V (a +bX) = b2V(X) (3) E[X2] = \sigma 2 X +µ2 X (4) V (aX +bY) = a2\sigma 2 X +2ab\sigma XY +b2\sigma 2 Y (5) cov(a + bX,Y) = b\sigma XY (6) cov(X,Y ) = E[XY]−µXµY

Name: let xy be discrete random variables let x and sigma 2 x be the mean and variance of x y and sigma 2 y be the mean and variance of y let sigma xy be the covariance between x and y let abc be 52892
Uploaded: 2024-07-31T01:52:06-08:00
Duration: 2 min 12 s
Channel: Adi S
Description: let xy be discrete random variables let x and sigma 2 x be the mean and variance of x y and sigma 2 y be the mean and variance of y let sigma xy be the covariance between x and y let abc be 52892

          Let X,Y be discrete random variables.
 Let µX and \sigma 2
 X be the mean and variance of X; µY and \sigma 2
 Y be the mean and variance of Y. Let
 \sigma XY be the covariance between X and Y. Let a,b,c be constants. Show the following: (HINT: Use
 the definitions first.)
 1
(1) E[a +bX] = a+bE[X]
 (2) V (a +bX) = b2V(X)
 (3) E[X2] = \sigma 2
 X +µ2
 X
 (4) V (aX +bY) = a2\sigma 2
 X +2ab\sigma XY +b2\sigma 2
 Y
 (5) cov(a + bX,Y) = b\sigma XY
 (6) cov(X,Y ) = E[XY]−µXµY

Added by Melissa S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/31/2024

Step 1

(1) \( E[a + bX] = a + bE[X] \) ** Show more…

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Let X,Y be discrete random variables. Let µX and \sigma 2 X be the mean and variance of X; µY and \sigma 2 Y be the mean and variance of Y. Let \sigma XY be the covariance between X and Y. Let a,b,c be constants. Show the following: (HINT: Use the definitions first.) 1 (1) E[a +bX] = a+bE[X] (2) V (a +bX) = b2V(X) (3) E[X2] = \sigma 2 X +µ2 X (4) V (aX +bY) = a2\sigma 2 X +2ab\sigma XY +b2\sigma 2 Y (5) cov(a + bX,Y) = b\sigma XY (6) cov(X,Y ) = E[XY]−µXµY