If X has a geometric distribution with θ = 1/3 , find the formula for the probability distribution of the random variable Y = 4 – 5X.
Answer to relevant QuestionsIf X is the total we roll with a pair of dice, for which the probability distribution is given on page 63, find the probability distribution of the remainder we get when the values of X are divided by 3. If X has a uniform density with α = 0 and β = 1, show that the random variable Y = –2 ∙ lnX has a gamma distribution. What are its parameters? 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. Consider two independent random variables X1 and X2 having the same Cauchy distribution Find the probability density of Y1 = X1 + X2 by using Theorem 7.1 (as modified on page 216) to determine the joint probability density ...Use the moment-generating function technique to rework Exercise 7.27. In exercise If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and θ and n2 and θ, show that ...
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