The previous exercise gave the formula for the standard deviation of a discrete random variable X. Let’s look at a simple case. Suppose X is a binary random variable where X = 1 with probability p and X = 0 with probability (1 - p).
a. Show that the mean of X is equal to p. 

b. Since (x - ц)² equals (0 - p)² = p² when x = 0 and (1 - p)² when x = 1, derive that σ² = p(1 - p) and σ = √p(1 - p), the special case of the binomial s with n = 1.