Suppose that X and Y have a joint pdf f (x, y) = (2/3)(x + 1), for 0 < x < 1,0 < y < 1, zero otherwise. (a) Find fx(x) (b) Find fy (у) (c) Find f(y|x) (d) Find P(X < 2Y < 3X) (e) Are X and Y independent? (f) Find E(Y|X) (g) Find Var(Y) (h) Find Var(E(Y|X)).

You may need to use the appropriate appendix table to answer this question. Suppose that the average price for a gallon of gasoline in the Country A is $3.74 and in Country B it is $3.40. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the Country A and a standard deviation of $0.20 in Country B. (a) What is the probability that a randomly selected gas station in Country A charges less than $3.50 per gallon? (Round your answer to four decimal places.) (b) What percentage of the gas stations in Country B charge less than $3.50 per gallon? (Round your answer to two decimal places.) (c) What is the probability that a randomly selected gas station in Country B charged more than the mean price in the Country A? (Round your answer to four decimal places.)

What is the value of x? X + 22=65

Solve the equation.