Currently very confused about lecture problems, please explain thoroughly, thank you!

Problem 1

The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 5.95 ounces and a standard deviation of 0.11 ounce. Suppose that you draw a random sample of 37 cans. Find the probability that the mean weight of the sample is less than 5.92 ounces. Probability =The joint probability mass function of X and Y is given by p(1, 1) = 0 p(1, 2) = 0.05 p(1, 3) = 0.1 p(2, 1) = 0.05 p(2, 2) = 0.1 p(2,3) = 0.05 p(3, 1) = 0.05 p(3, 2) = 0.05 p(3, 3) = 0.55 (a) Compute the conditional mass function of Y given X = 1: P(Y = 1/X = 1) = P(Y = 2|X = 1) = P(Y = 3[X = 1) = (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X + Y > 4) = P(XY = 2) = P( * > 1) =A statistician uses Chebyshev's Theorem to estimate that at least 15 % of a population lies between the values 5 and 12. Use this information to find the values of the population mean, / , and the population standard deviation o. a) u = b) o =The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0, 12]. You observe the wait time for the next 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2 decimal places) that the sum of the 95 wait times you observed is between 536 and 637? Part b) What is the approximate probability (to 2 decimal places) that the average of the 95 wait times exceeds 6 minutes? Part c) Find the probability (to 2 decimal places) that 92 or more of the 95 wait times exceed 1 minute. Please carry answers to at least 6 decimal places in intermediate steps. Part d) Use the Normal approximation to the Binomial distribution (with continuity correction) to find the probability (to 2 decimal places) that 56 or more of the 95 wait times recorded exceed 5 minutes.The random variables X and Y have joint probability distribution specified by the following table: y=0 y=1 y=2 10 D=1 0 Please provide all answers to the following to three decimal places. (a) Find the expectation of XY. (b) Find the covariance Cov(X, Y) between X and Y. (c) What is the correlation between X and Y? (d) Suppose the random variables X and Y above are connected to random variables U and V by the relations X = 6U + 6 Y = 9V +4 What is the covariance Cov(U, V)? (e) What is the correlation between U and V