The probability distribution data is in the other image.

Consider the discrete probability distribution shown to the right, and complete parts a through e below. a. Calculate the variance and standard deviation of the random variable 62 = (Round to two decimal places as needed.) b) Let y = x + 2. Calculate the variance and standard deviation of the random variable y. oy = 0 (Round to two decimal places as needed.) c) Let z = 2x. Calculate the variance and standard deviation of the random variable z (Round to two decimal places as needed.) 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. A. Adding a constant, c, decreases its variance by a multiple of c and decreases its standard deviation by a multiple of c B. Adding a constant, c, increases its variance by a multiple of c and increases its standard deviation by a multiple of c- O C. Adding a constant, c, to a random variable has no effect on its variance and standard deviation. D. Adding a constant, c, increases its variance by a multiple of c and increases its standard deviation by a multiple of c. . 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. A. Multiplying a random variable with a constant, c, increases its variance by a multiple of c and increases its standard deviation by a multiple of off. B. Multiplying a random variable with a constant, c, increases its variance by a multiple of c and increases its standard deviation by a multiple of c. C. Multiplying a random variable with a constant, c, decreases its variance by a multiple of c and decreases its standard deviation by a multiple of c O D. Multiplying a random variable with a constant, c, has no effect on its variance and standard deviation.X P(x) 0. 15 0.35 27 0.50