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Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and variance of 2. Let S=X+Y, calculate E(S) and Var(S). Let Z=2Y^2+1/2 X+1 calculate E(Z). Hint: for any random variable X, we have Var(X)=E(X-E(X))^2=E(X^2 )-(E(X))^2, you may want to find EY^2  with this. Calculate cov(S,X). Hint: similarly, we have cov(Z,X)=E(ZX)-E(Z)E(X),

Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and variance of 2. Let S=X+Y, calculate E(S) and Var(S). Let Z=2Y^2+1/2 X+1 calculate E(Z). Hint: for any random variable X, we have Var(X)=E(X-E(X))^2=E(X^2 )-(E(X))^2, you may want to find EY^2  with this. Calculate cov(S,X). Hint: similarly, we have cov(Z,X)=E(ZX)-E(Z)E(X),

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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  1. Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and variance of 2.
    • Let S=X+Y, calculate E(S) and Var(S).
    • Let Z=2Y^2+1/2 X+1 calculate E(Z). Hint: for any random variable X, we have Var(X)=E(X-E(X))^2=E(X^2 )-(E(X))^2, you may want to find EY^2  with this.
    • Calculate cov(S,X). Hint: similarly, we have cov(Z,X)=E(ZX)-E(Z)E(X),
    • Calculate cov(Z,X).
    • Are Z and X independent? Are Z and Y independent? Why?
    • What about mean independence?
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