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- A restaurant serves three fixed-price dinners costing $11, $14, and $19. For a randomly selected couple dining at this restaurant, let X = the cost of the man's dinner and Y = the cost of the woman's dinner. The joint pmf of X and Y is given in the following table. X Px(x) p(x, y) 11 14 19 X (a) Compute the marginal pmf of X. y Py(y) 11 y 14 19 0.10 0.35 0.10 0.10 11 0.05 0.00 0.20 0.05 0.05 11 Compute the marginal pmf of Y. 14 14 19 19 (b) What is the probability that the man's and the woman's dinner cost at most $14 each? (c) Are X and Y independent? Justify your answer. O X and Y are not independent because P(x, y) = Px(x) Py(Y). X and Y are not independent because P(x, y) # Px(x) Py(Y). O X and Y are independent because P(x, y) = Px(x) · Py(Y). O X and Y are independent because P(x, y) # Px(x) · Py(Y). . (d) What is the expected total cost, in dollars, of the dinner for the two people? $ (e) Suppose that when a couple opens fortune cookies at the conclusion of the meal, they find…What is the expected value of a continuous random variable X with probability density function (pdf) given by f(x) = 2x, 0 < x < 1?The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772
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