Truncated normal distributions: (a) Suppose that j ; N0; 1. Using Equations 20.14 (page 630) for the

Truncated normal distributions:

(a) Suppose that j ; Nð0; 1Þ. Using Equations 20.14 (page 630) for the mean and variance of a left-truncated normal distribution, calculate the mean and variance of j j j > a for each of a ¼ &2; &1; 0; 1; and 2.

(b) 'Find similar formulas for the mean and variance of a right-truncated normal distribution. What happens to the mean and variance as the threshold moves to the left?