Question
11. Economic conditions cause fluctuations in the prices of raw commodities as well as in finished products. Let X denote the price paid for a
11. Economic conditions cause fluctuations in the prices of raw commodities as well as in finished products. Let X denote the price paid for a barrel of crude oil by the initial carrier, and let Y denote the rice paid by the refinery purchasing the product from the carrier. Assume that the joint density for (X, Y) is given by
fxy(x, y) = c ; 20 < x < y <40
(a)Find the value of c that makes this a joint density for a two-dimensional randomvariable.
(b)Find the probability that the carrier will pay at least $25.00 per barrel and the refinery will pay at most $30.00 per barrel for the oil.
(c)Find the probability that the price paid by the refinery exceeds that of the carrier by at least &10.00 per barrel.
(d)Find the marginal densities for X and Y.
(e)Find the probability that the price paid by the carrier is at least$25.00.
(f ) Find the probability that the price paid by the refinery is at most $30.00.
(g) Are X and Y independent? Explain.
43. Consider Exercise 11:
a. Find the curve of regression of X on Y. Is the regression linear?
b. Find the mean price paid by the carrier given that the refinery price is 30 dollars per barrel.
c. Find the curve of regression of Y on X. Is the regression linear?
d. FInd the mean price paid by the refinery for a barrel of crude oil given that the carrier paid 35 dollars per barrel.
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