g 1. Suppose X is a uniform random variable over [0,1] ( i. e., X v U [0; 1]) and Y is a Bernoulli random variable with a success probability Pr(Y = 1) = 0:5, i:e:; Y = ? 1; with probability 0.5 0; with probability 0.5 : Compute the following (You will not need any program for this problem, just solve by hands after your readings.) ? Pr(X < 0:1) and Pr(Y < 0:1) ? E(X); V ar(X); E(Y ) and V ar(Y ) ? E (0:3X + 0:7Y ) and E (0:5X + 0:5Y ) ? For any 2 [0; 1]; E( X + (1 )Y ) ? Now suppose X and Y represent (statistically independent) outcomes of two lotteries, and you would like to invest your $100 to these lotteries. Assume you only care about the mean (preferably high) and variance (preferably low) of your investment. How