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.

Jose bought 20 shares of netflix at the close price of $117.98. in a few years, jose sells all of his shares at $128.34. how much money did jose make? a.) $192.50 b.) $207.20 c.) $212.50 d.) $224.60

How much orange juice do you need to make 2 servings of lemony orange slush?

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?