Consider the following discrete probability distribution:

x P(x)

3 0.13 6 0.12 9 0.15 12 0.60

a. Calculate the variance and standard deviation of the random variable.

b. Let y = x + 7. Calculate the variance and standard deviation of the random variable y.

c. Let z = 7x. Calculate the variance and standard deviation of the 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 its variance and standard deviation.

e. From your calculations in part a and part

c, indicate the effect that multiplying a random variable with a constant has on the variance and the standard deviation of the random variable.