7. Sixty percent of large purchases made at a certain com- puter retailer are personal computers, 30% are laptop computers, and 10% are peripheral devices such as printers. As part of an audit, one purchase record is sampled at random. a. What is the probability that it is a personal computer? b. What is the probability that it is either a personal computer or a laptop computer?asticities of Demand 1. A. Steel Supply and Demand for USA are given by ; Demand: P = 1,200 -100 (QD) and supply: P = 100 (QS) where QD = quantity demanded and QS = quantity supplied 1. Draw the market supply and demand curves. What are the equilibrium price and equilibrium quantity? 2. Compute the price elasticity of demand when price is $500. What can you say about the demand?l. (2 pts each) True/False questions. (a) If X is a normal random variable with mean 3 and variance 4, then 2X 6 is also a normal random variable with mean 0 and variance 8. (b) Suppose that random variable X has mean 2 and variance 3, and random variable Y has mean 1 and variance 1. Then Z = 2X + 31' 5 has mean2 andvariance 21. (c) Given three random variables X, Y, Z, if X and Y are independent, X and Z are independent, then Y and Z are also independent. (d) Let X be a continuous random variable with possible values in [0, 1]. Let Y be another continuous random variable with possible values in [0, 2]. Then Y must have a larger variance than X. (e) In order to model a proportion. it is a good choice to use gamma distributions. Consider the model below describing the supply and demand for bananas. Q5 = Bo + BB+ US (1) Q? = Qo + mili+ Up (2) P; is the price of banana, Q; is the supply of banana, @? is the demand of banana. UP and UP are mutually independent IID random variables with a mean of zero, and variances equal to o?, and of, respectively. Of = QP is the market equilibrium condition. (a) Show that P, and UP are correlated. (15 points) (b) Show that the OLS estimator of on is biased. (5 points) Now, We add a new explanatory variable Y, into the demand function of banana. Y, describes the income level and is exogenous which means Y is uncorrelated with both UP and US. Of = Bo + BIR:+ US (3) Q? = an+ on Pi + 02Vi+ UP (4) (c) With equation (3) (4) and the market equilibrium condition, write Q = ng+ xiY, +e;. Find ag, x1, and e; as functions of Bo, 81, 00, 01, 02, US, and UP. (10 points)