Question: 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.