Consider the situation of Review Exercise 3.75. But suppose the joint distribution of the two proportions is given by f(x1, x2) = 6x2, 0 < x2 < x1 < 1, 0, elsewhere.  (a) Give the marginal distribution fX1 (x1) of the proportion X1 and verify that it is a valid density function.  (b) What is the probability that proportion X2 is less than 0.5, given that X1 is 0.7?.

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3.76 Consider the situation of Review Exercise 3.75. But suppose the joint distribution of the two proportions is given by f(x1, x2) = 6x2, 0 < x2 < x1 < 1, 0, elsewhere. 

(a) Give the marginal distribution fX1 (x1) of the proportion X1 and verify that it is a valid density function

(b) What is the probability that proportion X2 is less than 0.5, given that X1 is 0.7?.

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