1. (22 points) In addition to estimating the official (U-3) U.S. unemployment rate that you heard about in class, the BLS also estimates a number of alternative measures of \"labor underutilization.\" One of these, the U-6 rate, uses a broader denition of the labor force, and measures the proportion of this broader labor force that is either unemployed or is working part-time but would like to work more hours. This is sometimes called the \"underemployment rate.\" Suppose the true underemployment rate is 20 percent (levels this high were seen early in the pandemic). You plan to survey four members of the labor force at random. Let X,- be the underemployment status (1 if underemployed, 0 otherwise) of the ith member of your survey, and let )3 be the proportion of your sample that is underemployed. 1.1. What is P(X,- = 0)? 1.2. What is P(X,- = 1)? 1.3. What is P@ = 0)? 1.4. What is P( = i)? 1.5. What is P( = 5? 1.6. What is P( = g)? 1.7. What is P( = 1)? 1.8. What is E(X,-)? 1.9. What is E()? 1.10. What is sd(X,-)? 1.11. What is sd(f.i)