If X has a uniform density with α = 0 and β = 1, show that Y = X– 1/ a with a> 0 has the Pareto distribution of Exercise 6.21 on page 184.
Answer to relevant QuestionsIf the probability density of X is given by And Y = X2, find (a) The distribution function of Y; (b) The probability density of Y. If the joint probability distribution of X and Y is given by f(x, y) = (x– y)2 / 7 for x = 1, 2 and y = 1, 2, 3, find (a) The joint distribution of U = X + Y and V = X – Y; (b) The marginal distribution of U. Rework Exercise 7.30 by using Theorem 7.2 to determine the joint probability density of Z = XY2 and U = Y and then finding the marginal density of Z. If the joint probability density of X and Y is given by And Z = √X2 + Y2, find (a) The distribution function of Z; (b) The probability density of Z. With reference to Exercise 3.93 on page 107, find the probability density of the average mileage of two such tires. Assume independence.
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