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- 3. Suppose that X is a continuous random variable with pdf 3x², 04. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.Example 2.17 Let X be a continuous type random variable with PDF given as 1 = (x)f 27 Let Y be another random variable such that Y = X². Find the PDF of Y.5. (8 pts) X is a random variable with pdf Xe-xx>0 f(x) = { o/w and let Y = 1-X/2. Find the pdf of Y with the support of g(y).3.2.13 Y is a continuous random variable with { 2(1- y), 0< y < 1; fy(4) = { 0, otherwise. Derive Fy(t).EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.21. Let the random variable X have the moment generating function e3t M(t) : -1Example 2.7. Let X and Y be jointly continuous random variables with joint PDF is given by: fx,Y (x, y) = (6/5)(æ² + y))I(o,1)(x)I(0,1)(4) 1. Show the marginal PDF of X. 2. Find P(X > Y). 3. Find P( < X < }).6. (b)Suppose that X has moment generating function Mx(t) = ( et +) (i) Find the p.m.f. of X. (ii)Find the mean and variance of X.B) Let the random variable X have the moment generating function e3t M(t) for -1The p.d.f. of a random variable X' is as shown in the figure. The pdf is zero for X 5. Calculate (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X. fx (x) kb) A random variable X follows an exponential distribution, X~Exp(0), with parameter 0 > 0. Find the cumulative distribution function (CDF) of X. i) ii) Show that the moment generating function (MGF) of X is M(t) = iii) Use the MGF in (ii) to find the mean and variance of X.SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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