Equations XXXXXXXXXXon page 631) give formulas for the mean and variance of a left-censored normally distributed variable. (These formulas are also shown in the preceding exercise.) Derive similar...

Equations 20.16 (on page 631) give formulas for the mean and variance of a left-censored normally distributed variable. (These formulas are also shown in the preceding exercise.) Derive similar formulas for (a) a right-censored and (b) an interval-censored normally distributed variable.

Using Equations 20.17 (page 631) for the incidentally truncated bivariate-normal distribution, show that the expectation of the error ε_i
in the Heckman regression model (Equations 20.18 and 20.19 on page 632) conditional on Y being observed is