Equally Likely Integers: Mean and Standard Deviation Assume that a probability distribution is described by the discrete random variable x that can assume the values 1, 2, . . . , n, and those values are equally likely. This probability distribution has mean and standard deviation described as follows.

a. Show that m 5 (n 1 1) 2 for the case of n 5 5.

b. Show that for the case of n 5 5.

c. In testing someone who claims to have ESP, you randomly select whole numbers between 1 and 20, and the random variable x is the number selected. Find the mean and standard deviation for x.