STATS Six Questions

1. The following table lists the bivariate distribution of X and Y.XY 1 21 .5 .12 .1 .3a) Find the marginal probability distribution of Xb) Find the marginal probability distribution of Yc) Compute the mean and variance of Xd) Compute the mean and variance of Y2. When trucks arrive at the Ambassador Bridge , each truck must be checked by customs agents. The times are exponentially distributed with a service rate of 10 per hour. What is the probability that a truck requires more than 15 minutes to be checked?3. A student takes a pop quiz that consists of three true-false questions. Each question can be answered correctly (C) or incorrectly (I). Consider this to be a three-step process; i.e., answering the first question with a C or an I, answering the second question with a C or an I, and answering the third with a C or an I.a) Identify each sample space outcome using the C and I designations.b) What is the probability that the student gets all three questions correct?c) What is the probability that the student gets exactly two questions correct?d) What is the probability that the student gets at least two questions correct?4. The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours.a) What is the probability that a randomly selected North American adult watches television for more than 7 hours per day?b) What is the probability that the average time watching television by a random sample of five North American adults is more than 7 hours per day?c) What is the probability that in a random sample of 5 North American adults, all watch television for more than 7 hours per day?5. The female instructors at a large university recently lodged a complaint about the most recent round of promotions from assistant professor to associate professor. An analysis of the relationship between gender and promotion was undertaken which produced the joint probabilities in the following table:Promoted Not PromotedFemale .03 .12Male .17 .68a) What is the rate of promotion among female assistant professors?b) What is the rate of promotion among male assistant professors?c) Is it reasonable to accuse the university of gender bias?6. The random variable X is exponentially distributed with ? = .5. Find the following probabilities.a) P(X > 1)b) P(X > .4)c) P(X < .5)d) P(X < 2)