**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 $ P(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.

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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Year Returns X Y 116% 22% 2 30 31 3-23-28 4 11 12 5 10 22 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not round intermediate calculations. Enter your average return and standard deviation answers as a percent rounded to 2 decimal places, e.g., 32.16. Enter your variance answers rounded to 5 decimal places, e.g., 16161.)
(c) The price of a 14 oz cup of coffee in Sunshine cafés is a random variable C with an expected value of $3.00 and a standard deviation of $1. At any given shop, the price doesn't vary, but it varies independently across shops. Tomorrow morning, you plan to buy two 14 oz cups of coffee from the same shop while your friend plans on buying two from two different shops. (i) How much do you expect to spend on coffee tomorrow and with what standard deviation? (ii) How much do you expect your friend to spend and with what standard deviation? (iii) Who do you think has a better idea and why?
A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation of 44 ounces. What is the probability of filling a cup between 21 and 31 ounces? Round your answer to four decimal places.
An estimator () is said to be a consistent estimator if the bias of (✔) goes to zero as the sample size gets larger and larger and the variance goes to zero. O True False
A bakery has determined that the number of loaves of its white bread demanded daily has a normal distribution with mean 7,200 loaves and standard deviation 300 loaves. Based on cost considerations, the company has decided that its best strategy is to produce a sufficient number of loaves so that it will fully supply demand on 94% of all days. a. How many loaves of bread should the company produce? b. Based on the production in part (a), on what percentage of days will the company be left with more than 500 loaves of unsold bread?
ii) Suppose that you find out that you have an OLS estimator which is unbiased but has a non-minimum variance. Discuss two practical steps that you take to reduce the variance of your OLS estimator. Explain your reasoning.
In a hypothetical country called Tritonland, demand and supply of fish are determined by the following system of equations: Q Q = 3+P+v, where Q and P stand for quantity and price respectively, and that u and v are independent Uniform [0, 2]. Suppose we have i.i.d. observations (Qi, Pi)_1 from n markets in equilibrium. Answer the next few questions. = 15 P+u,
Please do not give solution in image format thanku
Question 3 Saved 4) Listen A customer service team receives an average of 376 emails every day. Assume that the standard deviation for the number of emails is 96 emails. A random sample of 40 days was selected. a. What is the expected value of the sample mean? b. What is the standard deviation of the sample mean? Round your answer to two decimal places (e.g. 2.12). c. What is the probability that the average number of emails received was between 360 and 372? Round your answer to two decimal places with a leading zero (e.g. 0.18).
A campus finance officer finds that, for all parking tickets issued, fines are paid for 78% of the tickets. The fine is $2. In the most recent week, 620 parking tickets have been issued.a. Find the mean and standard deviation of the number of these tickets for which the fines will be paid.b. Find the mean and standard deviation of the amount of money that will be obtained from the payment of these fines.
Using the normal distribution table find ZO such that: P(Zs- Zo) = .0132 1.96 -1.64 -2.22 2.17