please do both problems and detail all steps!

Question \#5: Three different roads feed into a particular freeway entrance. Suppose that during a fixed time period, the number of cars coming from each road onto the freeway is a random variable, with expected value and standard deviation as given in the table. a) What is the expected total number of cars entering the freeway at this point during the period? [Hint: Let Xi= the number from road i.] b) What is the variance of the total number of entering cars? Have you made any assumptions about the relationship between the numbers of cars on the different roads? c) With X denoting the number of cars entering from road i during the period, suppose that Cov( X1,X2)=70,Cov(X1,X3)=80, and Cov(X2,X3)=90 (so that the three streams of traffic are not independent). Compute the expected total number of entering cars and the standard deviation of the total. Question \#6: A restaurant serves three fixed-price dinners costing $12,$15, and $20. For a randomly selected couple dining at this restaurant, let X=5 the cost of the man's dinner and Y=5 the cost of the woman's dinner. The joint pmf of X and Y is given in the following table: a) Compute the marginal pmf's of X and Y. b) What is the probability that the man's and the woman's dinner cost at most $15 each? c) Are X and Y independent? Justify your answer. d) What is the expected total cost of the dinner for the two people? e) Suppose that when a couple opens fortune cookies at the conclusion of the meal, they find the message "You will receive as a refund the difference between the cost of the more expensive and the less expensive meal that you have chosen." How much would the restaurant expect to refund