Let's consider r.v.s X and Y and a continuous bivariate distribution f(X,Y) defined by f(x, y) = { 3.x 0 for0≤y≤x≤1 otherwise a.) Find the marginal distribution of X. b.) Find the marginal distribution of Y. c.) Find дx and Var(X) d.) Find #y and Var(Y) e.) Find Cov(X,Y) f.) Define Z = 2X – Y. Find E(Z) and Var(Z)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Let's consider r.v.s X and Y and a continuous bivariate distribution f(X,Y) defined by
f(x, y) =
{
3.x
0
for0≤y≤x≤1
otherwise
a.) Find the marginal distribution of X.
b.) Find the marginal distribution of Y.
c.) Find дx and Var(X)
d.) Find #y and Var(Y)
e.) Find Cov(X,Y)
f.) Define Z = 2X – Y. Find E(Z) and Var(Z)
Transcribed Image Text:Let's consider r.v.s X and Y and a continuous bivariate distribution f(X,Y) defined by f(x, y) = { 3.x 0 for0≤y≤x≤1 otherwise a.) Find the marginal distribution of X. b.) Find the marginal distribution of Y. c.) Find дx and Var(X) d.) Find #y and Var(Y) e.) Find Cov(X,Y) f.) Define Z = 2X – Y. Find E(Z) and Var(Z)
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