4. Let X and Y be independent, continuous random variables with densities {}} and fx(x) = fy (y) = = {}² if 0 < x < 2 otherwise. y if 0 < y < 2 otherwise. (a) Compute the density of X+Y. (b) Let Z = ¹ (X+Y) (that is, the Z is the average of X and Y). What is the density of Z?

Q: Suppose that X and Y are continuous random variables with joint pdf f (x, y) = e-**) 0<x<∞ and 0 < y…

A: Introduction: The joint density function of two random variables X and Y is given below:

Q: Suppose that the random variable X has density fx (x) = 4x³ for 0 X).

A: Independence of pdf applied.

Q: Let X be a continuous random variable with density f (x) = 24x-4 for æ > 2. Then Var (X) is equal to

A:

Q: 3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ +…

A:

Q: 1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of…

A: Let x be a uniform random variable in the interval (0, 1).