# Marginal and conditional density

A tobacco company produces blends of tobacco with each blend containing various proportions of Turkish, domestic and other tobacco.

The proportion of Turkish and domestic in a blend are random variables (X = Turkish and Y = domestic) with joint density function

f (x,y) = { 24xy, 0 < or= x < or=1, 0 < or = y < or=1

x + y < or=1

0, elsewhere

A. Find the marginal density for the proportion of the domestic tobacco.

B. Find the conditional density of X given Y = 3/4

C. Find the probability that the proportion of Turkish tobacco is less than 1/8, given that the blend contains 3/4 domestic tobacco.

PLEASE SEE ATTACHED FILE FOR CLEARER, TYPED COPY OF THE QUESTION.

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#### Solution Summary

The solution shows how to find marginal and conditional density for a given situation.