Problem 2. (SW 11.8(a-c)) Consider the linear probability model Y₁ = Bo+B₁X₂ + Uį, and assumethat E(u₂|X;) = 0.(a) Show that Pr(Y₁ = 1|X₂) = Bo + B₁X₁.(b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (Bo + B₁X;)]. [Hint: You will need the formula for thevariance of a Bernoulli variable, see, e.g., SW Equation (2.7).](c) Is u heteroskedastic? Explain.

Answered: Image /qna-images/answer/75ca2087-105f-480e-b635-666874a867fe.jpg

(a) Show that Pr(Yį = 1|X) = Bo+®ıX. (b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (Bo + B₁X;)]. [Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).] (c) Is u, heteroskedastic? Explain.

(a) Show that Pr(Yį = 1|X) = Bo+®ıX. (b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (Bo + B₁X;)]. [Hint: You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).] (c) Is u, heteroskedastic? Explain.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

Problem 2. (SW 11.8(a-c)) Consider the linear probability model Y₁ = Bo+B₁X₂ + Uį, and assume
that E(u₂|X;) = 0.
(a) Show that Pr(Y₁ = 1|X₂) = Bo + B₁X₁.
(b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (Bo + B₁X;)]. [Hint: You will need the formula for the
variance of a Bernoulli variable, see, e.g., SW Equation (2.7).]
(c) Is u heteroskedastic? Explain.

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