Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers.The joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y,, the proportion of the capacity sold during the week, is given by[3y1 0 s y2 s Y1 s 1,F(Y1• Y2) = {1*elsewhere.(a) Find the marginal density function for Y,.f2(Y2) =, where(b) For what values of y, is the conditional density f(y, ly,) defined?(c) What is the probability that more than half a tank is sold given that six-sevenths of a tank is stocked? (Enter your probability as a fraction.)

Answered: Image /qna-images/answer/709a64f6-e0fd-4d8d-9ab2-8ea338a2c4a7.jpg

Answered: (a) Find the marginal density function…

A First Course in Probability (10th Edition)

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a) Find the marginal density function for Y,. f2(Y2) = , where (b) For what values of y, is the conditional density f(y,ly,) defined? in (c) What is the probability that more than half a tank is sold given that six-sevenths of a tank is stocked? (Enter your probability as a fraction.)