A restaurant serves three fixed price dinners costing $12, $15
and $20. For a randomly selected couple 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 below.
|
y
|
|
p(x,y)
|
12
|
15
|
20
|
|
12
|
0.05
|
0.05
|
0.1
|
|
15
|
0.05
|
0.1
|
0.35
|
|
20
|
0.00
|
0.2
|
0.1
|
(a) What is the probability that the man’s and the woman’s
dinner cost at most $15 each?
(b) Are X and Y independent?
(c) Find P(X = Y|Y ≥ 15)?
(d) Suppose that when a couple opens fortune cookies at the end
of their meals, they find the message You will receive as refund
the difference between the cost of the more expensive and the less
ex- pensive meal that you have chosen. How much does the restaurant
expect to refund?
dr.two
