Mathematics 1550H – Introduction to probability Trent University, Winter 2016 Assignment #4 (Un)expected Value Due on Friday, 1 Monday, 4 April, 2016. 1. Verify that f(t) = 1 π (1 + t 2) is a probability density function, but that a random variable X that has f(t) as its probability density does not have a finite expected value.  Hint: Try computing E(X) and see what you get . . . 2. Find a function g(t) such that a random variable X which has g(t) as its probability density function has a finite expected value, but does not have a finite variance.