1. Let X and Y be two jointly continuous random variables with joint pdf f(x,y) = {k(x+y), 0≤x≤ 1,0 ≤ y ≤1 otherwise a. Find the constant k. b. Find the marginal pdf of X. c. Find E(X).

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1. Let X and Y be two jointly continuous random variables with joint pdf
f(x,y) = {k(x +3
y),
0≤x≤ 1,0 ≤ y ≤ 1
otherwise
a. Find the constant k.
b. Find the marginal pdf of X.
c. Find E(X).
d. Find Var(X).
e. Find P(1/2 < X < 1,0 < Y < 1/2).
Transcribed Image Text:1. Let X and Y be two jointly continuous random variables with joint pdf f(x,y) = {k(x +3 y), 0≤x≤ 1,0 ≤ y ≤ 1 otherwise a. Find the constant k. b. Find the marginal pdf of X. c. Find E(X). d. Find Var(X). e. Find P(1/2 < X < 1,0 < Y < 1/2).
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