1.Most days you are good. But some days you are bad. Each day there is a 99% chance you are good and a 1% chance you are bad. If you are bad 3 times, you are 'out' and you go to prison. On average, how many days until you go to prison?
2.You are a party animal. Your two best friends George and Ziyi like to buy you beer. The number of beers that George buys you is a random variable G with mean 3.0. The number of beers that Ziyi buys you is a random variable Z with mean 4.2. You are downtown and are equally likely to run into either George or Ziyi (but not both). G and Z are independent.
Let F be the number of beers your friend buys you.
a) Express F as a function of three random variables: G, Z, and B~Bin(1,1/2), where all 3 are mutually independent.
b) compute the expected value of F.
3. Let X be a random variable with two outcomes, x1, x2 having probabilities p1, p2, respectively, so that p1+p2 = 1. Assume in addition that mean, E(X)=0 and Var(X) = 1
Show, by finding three different examples of such X, that this information is not enough to determine X.