Help with 4.30 - 4.32 please! ### Probability and Statistics Questions#### Question 4.29What is \( E(X + Y|Z = 10) \)?- a. 40- b. 45- c. 50- d. 55#### Use the following information for the next 3 questions:Suppose that we have three random variables \( X \), \( Y_1 \), and \( Y_2 \). \( Y_1 \) and \( Y_2 \) are from an identical distribution and independent to each other:- \( \text{Var}(X) = 5 \)- \( \text{Var}(Y_i) = 8 \) for \( i = 1, 2 \)#### Question 4.30What is \( \text{Var}(X + Y_1) + \text{Var}(X - Y_2) \)?- a. 20- b. 23- c. 26- d. 29#### Question 4.31If \( \text{Var}(aX) + \text{Var}(Y_1 + Y_2) = 36 \), what is \( \text{Var}(a(Y_1 + Y_2)) \)?- a. 16- b. 32- c. 48- d. 64#### Question 4.32If \( \text{Var}(X + Y_1 + Y_2) = 25 \), what is \( \text{Cov}(X, Y_i) \) for \( i = 1, 2 \)?- a. 1- b. 2- c. 3- d. 4#### Question 4.33Suppose that we have two random variables \( X \) and \( Y \). Which of the following is NOT true?- a. If \( X \) and \( Y \) are independent, \( \text{Corr}(X, \eta) = 0 \).- b. If \( \text{Corr}(X, \eta) = 0 \), \( X \) and \( Y \) are independent.- c. If \( E(Y) = 0 \), \( \text{Cov}(X, \eta) = E(XY) \).- d.

Name: Help with 4.30 - 4.32 please! ### Probability and Statistics Questions
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: Help with 4.30 - 4.32 please! ### Probability and Statistics Questions#### Question 4.29What is \( E(X + Y|Z = 10) \)?- a. 40- b. 45- c. 50- d. 55#### Use the following information for the next 3 questions:Suppose that we have three random variables