# Question: Compute E X if X has a density function given by a b c

Compute E[X] if X has a density function given by

(a)

(b)

(c)

(a)

(b)

(c)

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The density function of X is given by If E[X] = 3/5, find a and b. Use the identity of Theoretical Exercise 5 to derive E[X2] when X is an exponential random variable with parameter λ. Theoretical Exercise 5 Use the result that, for a nonnegative random variable Y, to show that, for a ...Compute the hazard rate function of a gamma random variable with parameters (α, λ) and show it is increasing when α ≥ 1 and decreasing when α ≤ 1. Show that Z is a standard normal random variable, then, for x > 0, (a) P{Z > x} = P{Z < −x}; (b) P{|Z| > x} = 2P{Z > x}; (c) P{|Z| < x} = 2P{Z < x} − 1. Let f (x, y) = 24xy 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ x + y ≤ 1 and let it equal 0 otherwise. (a) Show that f (x, y) is a joint probability density function. (b) Find E[X]. (c) Find E[Y].Post your question