Suppose X and Y are independent random variables where X takes the value 0 with probability 0.5 and the value 1 with probability 0.5, and Y takes the value 1 with probability 0.1 and the value 10 with probability 0.9.
Use the following random variables to show that E(X/Y) ≠ E(X)/E(Y) (the expectation of the quotient is not equal to the quotient of the expectations) even when two random variables are independent. Use the harmonic mean (Exercises 21 and 22) to guess why the expectation of the quotient is bigger than the quotient of the expectations.