The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount Y from which a random a
mount X is sold during that day. Suppose that the tank is not resupplied during the day so that x ? y, and assume that the joint density function of these variables is f(x,y) = 2 for 0 < x < y < 1. find the that the amount of kerosene sold is between 0.25 and 0.50 thousands liters given that the amount in the tank at the start of the day is 0.90 thousands liters. (Hint: f(x|y) = f(x,y) / fy(y) ).
Find the marginal density for by integrating the joint PDF over all possible values of :
Then the density of conditioned on is
for and undefined elsewhere.
Thus
= = =
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