4.126 Work with a transformation. Here is a probability distribution for a random variable X:

Value of X 2 3
Probability 0.2 0.8

  1. (a) Find the mean and the standard deviation of this distribution.

  2. (b) Let Y = 5X −1. Use the rules for means and variances to find the mean and the standard deviation of the distribution of Y.

  3. (c) For part (b), give the rules that you used to find your answer.