A tobacco company produces blends of tobacco, with each
Chapter , Problem 2.103(choose chapter or problem)
A tobacco company produces blends of tobacco, with each blend containing various proportions of Turkish, domestic, and other tobaccos. The proportions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic) f(x, y) = 24xy, 0 x, y 1, x + y 1, 0, elsewhere. (a) Find the probability that in a given box the Turkish tobacco accounts for over half the blend. (b) Find the marginal density function for the proportion of the domestic tobacco. (c) Find the probability that the proportion of Turkish tobacco is less than 1/8 if it is known that the blend contains 3/4 domestic tobacco.
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