Problem 2. (SW 11.8(a-c)) Consider the linear probability model Y₁ = Bo+B₁X₁+u₁, and assume that E(u₂|X;) = 0. (a) Show that Pr(Y₁ = 1|X;) = Bo + B₁X₁. (b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (B₁ + B₁X₁)]. [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.
Problem 2. (SW 11.8(a-c)) Consider the linear probability model Y₁ = Bo+B₁X₁+u₁, and assume that E(u₂|X;) = 0. (a) Show that Pr(Y₁ = 1|X;) = Bo + B₁X₁. (b) Show that var(u₁|X₁) = (B₁ + B₁X₁)[1 − (B₁ + B₁X₁)]. [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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 2.** (SW 11.8(a-c)) Consider the linear probability model \( Y_i = \beta_0 + \beta_1 X_i + u_i \), and assume that \( E(u_i|X_i) = 0 \).
(a) Show that \( Pr(Y_i = 1|X_i) = \beta_0 + \beta_1 X_i \).
(b) Show that \( \text{var}(u_i|X_i) = (\beta_0 + \beta_1 X_i)[1 - (\beta_0 + \beta_1 X_i)] \). [*Hint:* You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).]
(c) Is \( u_i \) heteroskedastic? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b8a4ad9-b66e-4dbe-8b3f-39bf0adb3cae%2F8fdab33e-a988-477b-9d77-7f0092a50dd8%2Fu6crgq5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2.** (SW 11.8(a-c)) Consider the linear probability model \( Y_i = \beta_0 + \beta_1 X_i + u_i \), and assume that \( E(u_i|X_i) = 0 \).
(a) Show that \( Pr(Y_i = 1|X_i) = \beta_0 + \beta_1 X_i \).
(b) Show that \( \text{var}(u_i|X_i) = (\beta_0 + \beta_1 X_i)[1 - (\beta_0 + \beta_1 X_i)] \). [*Hint:* You will need the formula for the variance of a Bernoulli variable, see, e.g., SW Equation (2.7).]
(c) Is \( u_i \) heteroskedastic? Explain.
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