Truncated normal distributions (a) Suppose that j N0 1 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 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

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Question: Truncated normal distributions: (a) Suppose that j ; N0; 1. Using Equations 20.14 (page 630) for the mean and variance of a left-truncated normal distribution,

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?

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