Liniar combinations of random variables 1. Let X and Y be two continuous random variables with joint density function: a. Calculate P(X+Y ≥ !) b. Calculate E(Y-X) c. Calculate Var (Y - X). f(x,y)= 0

Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Is P(X > 2, Y < 3) equal to P(X > 2) × P(Y < 3)?

The multidimensional random variables H= (c) Let x := 2731 W 21 X2 Yı = follows N₁(μ, E) where 7 3 Y 2 3 Y 6 0 0 5 4 -2 2 4 -2 G (a) Determine all the independent univariate random variables. (b) What is the probability density function for x₁ + 2x₂? [2] tion density function p(y|x) and p(x|y = 1). and y := [₁]. Determine the conditional distribu-

2. Let X and Y denote independent random variables with respective probability density func- tions fx(x) = 2x, 0