Consider a set of n trials involving independent and identically distributed random variables X1;X2; : : : ;Xn; where the outcome of 1 corresponds to success and the outcome of 0 corresponds to failure, and the probability of success on each trial is p. (a) Show that E(Xi) = p, and Var(Xi) = p(1 p) for i = 1; 2; : : : ; n. (b) Let Y = X1 +X2 +: : :+Xn: Show that E(Y ) = np, and Var(Y ) = np(1p). (c) Let ^p = Y=n. Show that E(^p) = p, and Var(^p) = p(1 p)=n. Use facts from lecture notes and/or the Lohr Appendix handout to justify your reasoning for these problems.

At store a, erasers are sold individually. the cost y of x erasers is represented by the equation y=0.75x. the costs of erasers at store b are shown in the graph.

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)

How much is $1200 worth at the end of1 year,if the interest rate is 5.5% is compounded quarterly.