# Question: If X is an exponential random variable with mean 1

If X is an exponential random variable with mean 1/λ, show that

E[Xk] = k! / λk k = 1, 2, . . .

E[Xk] = k! / λk k = 1, 2, . . .

## Answer to relevant Questions

Show that If X is a beta random variable with parameters a and b, show that E[X] = a/a + b Var(X) = ab/(a + b)2(a + b + 1) The joint probability density function of X and Y is given by f (x, y) = e−(x+y) 0 ≤ x < ∞, 0 ≤ y < ∞ Find (a) P{X < Y} (b) P{X < a}. 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]. Jill’s bowling scores are approximately normally distributed with mean 170 and standard deviation 20, while Jack’s scores are approximately normally distributed with mean 160 and standard deviation 15. If Jack and Jill ...Post your question