11. Let X" be a random variable with the following probability distribution. Value x of X P(X=x) -2 0.10 0.05 0.45 0.25 0.15 Complete the following (a) Find the expectation E (X) of X. E(x) = 10 b) Find the variance Var(X') of X. var (x) - 0 12. Let X be a random variable with the following probability distribution. Value x of X P(X-x) -20 0.10 -10 0.20 0.05 10 0.20 20 0.20 30 0.25 Complete the following (a) Find the expectation E (X) of X. E(X) - 0 (b) Find the variance Var(X') of X. Var (X) = 0 3. Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, oroughly shuffle a standard deck of 52 cards (which is made up of 13 hearts, 13 spades, 13 ra to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, horoughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we nd gotten her suit guesses for each Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card. Answer the following. (a) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of the rele e relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. 0 4. Anita's, a fast-food chain s pecializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and : so on. Anita's reports that 45% of its customers order their food to go. Suppose that this proportion is correct and that a random sample of 50 individual customers is taken. Answer the following (a) Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response 5. The workers' union at a certain university is quite strong. About 96% of all workers employed by the university belong to the workers' union. ent on strike, and now a local TV station plans to interview a sample of 10 workers, chosen at random, to get their opinions on the strike Answer the following (a) Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantity the uncertainty of your estimate e standard deviation of the distribution. Round your response 6. Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed franchise locations, and go n. Anita's reports that 45% of its customer random sample of 4 customers at Anita's, exactly 2 order their food to go? der their food to go. If this proportion is correct, what is the probat probability that, in a nd your response to at least three decimal places. 17. A new surgery is successful? membersdeveloper wanted seeds will germinate. Suppose the manufacturer is correct. If 9 19. The workers' union at a particular university is quite strong. About 96% of all workers employed by the university belong to the ans to interview 4 workers (chose the probability that exactly 2 of the workers interviewed are union members? Round your response to at least three decimal places. 20. Suppose that 45% of all babies than 3 of them are girls? Carry your in