Hi, I am trying to do exercise 4.1.2 (attached).

Exercise 4.1.2. Proceeding from Exercise 4.1.1, suppose that the outgoing governor is allied with Wayne, but has agreed to endorse Lori if Wayne does not run. Let the random variable Z equal 1 when Lori secures this endorsement and equal 0 otherwise. Define Z as a mction on the state space 5. Construct a joint distribution table for X and Z. . Determine the marginal distribution of X. . Determine the conditional distribution of X when 2 = 0. What are the conditional mean and variance? e. Determine the conditional distribution of X when Z = 1. What are the conditional mean and variance? n-nsrp Exercise 4.1.1. Gubernatorial candidate Lori Middleton has hired a strategic marketing firm to help run her campaign. Lori is concerned about potential entry by two rivals, Brian Wayne and Lefty Jones, in the party's primary election. Their entry decisions will affect Lori's ability to raise funds and her advertising expenditures before the primary election. Let (S, P) denote Lori's probability model of the entry decisions of her rivals, and let the random variables X and Y describe Lori's fundraising and advertising expenditures before the primary. The probability model and the random variables are dened in the table below: probability P(s) realization X(s) realization Y(s) .20 10,000,000 1,500,000 .40 6,000,000 3,000,000 .10 6,000,000 3,000,000 .30 4,000,000 4,000,000 a. Construct a joint distribution table for X and Y. b. Compute the expected value and variance of X