Math 201 - Homework 7 Exercise 1. Choose a point uniformly at random from the triangle with vertices (0, 0), (0, 30), and (20, 30). Let (X, Y ) be the coordinates of the chosen point. (a) Find the cumulative distribution function of X. (b) Use part (a) to find the density of X. Let X be a random variable taking values {0, 1, 2, ...}. P (a) Show that E(X) = 1 k). k=1 P (X Exercise 2. (b) Assume now that X Geom(1/3), use the formula in (a) to calculate E(X). Exercise 3. The expectation of a random variable X is said to be finite if E(|X|) < 1. Find a continuous random variable that has finite expectation but infinite variance. Hint: Think of a function of the form x1n . 1