Find the standard deviation of the discrete random variable given in Table 1 from Example 2.

Approach We will use Formula (2a) with the unrounded mean μ_X = 2.39.

Approach We will use Formula (2b) with the unrounded mean μ_X = 2.39.

Formula 2

Data from Example 2

Suppose we ask a basketball player to shoot three free throws. Let the random variable X represent the number of shots made, so x = 0, 1, 2, or 3. Table 1 shows a probability distribution for the random variable X.

We denote probabilities using the notation P(x), where x is a specific value of the random variable. We read P(x) as “the probability that the random variable X equals x.” For example, P(3) = 0.51 is read “the probability that the random variable X equals 3 is 0.51.”

= V[(x - )2 P(x)] (2a) = Vx P(x)] Mx - (2b)