Consider the following discrete probability distribution:

x P(x)

5 0.10 10 0.15 15 0.25 20 0.50

a. Calculate the expected value of the random variable.

b. Let y = x + 5. Calculate the expected value of the new random variable y.

c. Let z = 5x. Calculate the expected value of the new random variable z.

d. From your calculations in part a and part

b, indicate the effect that adding a constant to a random variable has on the expected value of the random variable.

e. From your calculations in part a and part

c, indicate the effect that multiplying a random variable by a constant has on the expected value of the random variable.