I have trouble doing this question. It is from "Econometric Analysis 5th edition" by Greene. This question is from chapter 4, question 4. Thanks for any help.

Suppose that the regression model being estimated is

Yi = α + β1xi + ui

Where the disturbances ui have a probability density function fiven by

f (ui) = (1 / λ ) exp(-λui), ui ≥ 0

All the disturbances are then assumed to be non-negative

Show that

a) E(ui│xi) = λ

b) var(ui│xi) = λ2

c) The least squares estimate of β is unbiased, but the least squares estimate of α is biased

d) Suggest an application for this model