Question: 4.10 Suppose that Yi = b0 + b1Xi + ui, where (Xi, ui) are i.i.d., and Xi is a Bernoulli random variable with Pr(X =

4.10 Suppose that Yi = b0 + b1Xi + ui, where (Xi, ui) are i.i.d., and Xi is a Bernoulli random variable with Pr(X = 1) = 0.20. When X = 1, ui is N(0, 4); when X = 0, ui is N(0, 1).

a. Show that the regression assumptions in Key Concept 4.3 are satisfied.

b. Derive an expression for the large-sample variance of b n

1. [Hint:

Evaluate the terms in Equation (4.21).]

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