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- 22. If the random variable X - Exp(0), then what is the probability density function of the random variable Y = XVX?Suppose that Y is a random variable that takes on only integer values 1, 2, ... and has distribution function F(y). Show that the probability function p(y) = P(Y = y) is given by the following. F(1), p(y) = y = 1, Fly) - F(y - 1), y = 2, 3, ... Since Y takes on only non-negative integer values, when y > 1 we know P(Y = y) = p(y) can be written as p(y) = --Select- v. By definition F(y) = P(Y?y). And so p(y) = Select-- v. Finally, since Y 2 1 we know p(1) = --Select-- v. And so, we know p(1) = Select--Suppose that Y is a random variable that takes on only integer values 1, 2, ... and has distribution function F(y). Show that the probability function p(y) = P(Y = y) is given by the following. y = 1, p(v) = Fv) - Fly - 1), y = 2, 3, ... Since Y takes on only non-negative integer values, when y > 1 we know P(Y = y) = p(y) can be written as p(y) = -Select-- ♥. By definition F(v) = P(Y ? y). And so p(y) = -Select--- v. Finally, since Y 21 we know p(1) = -Select--v. And so, we know p(1) = ---Select-
- 2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?6. Suppose that the random variables X and Y have joint probability density function given by x+y, 07. If X is a random variable with fx ) = 1, 1b) A random variable Y has a probability density function defined as: -y 1 f(y)= 0 = e6) X is a continuous random variable with the following probability density function: fx(x) = 2x, 013-17. For the probability density function f(x) = 4(x + 4), over the given interval [6, 10], find the following: 13) E(X) 14) E(x²) 15) the mean 16) the variance 17) the standard deviation [ 14 LiFeRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning