Given here are the probability distributions of two random variables X and V.

(a) From the X distribution, determine the distribution of the random variable 8 - 2X and verify that it coincides with the Y distribution. (Hence, identify Y = 8 - 2X.)
(b) Calculate the mean and standard deviation of X (call these μY and σy, respectively).
(c) From the Y distribution, calculate the mean and standard deviation of Y (call these μY and σY, respectively).
(d) If Y = a + bX, then according to theory, we must have the relations σY = a + b μx and σY = |b| ax. Verify these relations from your results in parts (b) and (c).

y2431 y0246 x-1342 x-1234