If X1, X2, and X3 have the multinomial distribution (see Definition 5.8 on page 165) with n = 2, θ1 = 14 , θ2 = 13 , and θ3 = 5/12 , find the joint probability distribution of Y1 = X1 + X2, Y2 = X1 – X2, and Y3 = X3.
Answer to relevant QuestionsWith reference to Example 3.12 on page 82, find (a) The probability distribution of U = X + Y; (b) The probability distribution of V = XY; (c) The probability distribution of W = X – Y. 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. On page 215 we indicated that the method of transformation based on Theorem 7.1 can be generalized so that it applies also to random variables that are functions of two or more random variables. So far we have used this ...Use the result of Exercise 7.45 to show that, if n independent random variables Xi have normal distributions with the means µi and the standard deviations σi, then Y = α1X1 + α2X2 + · · · + anXn has a normal ...With reference to Exercise 3.102 on page 108, find the probability density of the random variable Z = X+ Y / 2 , which is the average of the two proportions of correct answers that a student will get on the two aptitude ...
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