6. Using the pdf of the random variable X and Y below. find the distribution of Z = XY. J,)={ 1 < x <∞. 1
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- The continuous random variable Y has the following pdf: 1- y?, 0Q. 4 Let X and Y be two continuous random variables with following joint probability density function SK (x² + y²); 0 Y), (c) P(X +Y > 1) (b)(a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of X = (ii) If 1 = 0, name the distribution of X given in 3(a)(i).The PDF of a random variable Y is Sy/2 0If 2 > 0 and X is a continuous random variable with p. d.f. 22xe-dx ,x 2 0 ,otherwise f(x) = Then var(X) is:Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 01. Which of the following is FALSE for a continuous random variable X with pdf y = f(x)? %3D A. P(6 S XS 9) = P(6 < X< 9) B. P(6 s XS 9) = f(6)+f(7)+f(8)+f(9) %3D C. P(6 < XS9) = area under the curve y=f(x) between 6 and 9 D. P(X = 9) = 0Give the answer for question 4Suppose W is a random variable with the pdf f(w) = 3u3e-w³/343 for w≥ 0.1 If Y = -12W + 11, what is the pdf of Y? еRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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