Question

View Edit Window Help Zoom Meeting Mock Exam.pdf 19 / 20 125% 19. (15 minutes) Let X be the random variable whose probability density function is the following: f(x) = ſo(1 – 2), if 0 < x < 1 10. otherwise (a) Find E[X] (b) Find the cumulative distribution function of X. 2 Online Timer timeandidate.com !!! Aps Google El

Answer 1

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19) Probability density function of X :- fla) e(1-x²) 0x< 1 D otherwise Let us find 'c'. we Now, know, / f(x) dx = 1 Sccl.a?)ana 1 Ida-casa dx = 1 os - 24 ce, e- c = a 5 X l' 2 5 x q=1 a) E(X) = x f(x) dx = a sá - x)dx 2 33 1 - 4 3 x 2/5 - 1/5 = 1/35 = 25 (Aus) b) F() = S Act) olt Sci-t²) at = 4 x - 1 x 3 (40a :f(n) a =0 %C4-29), o <x<! a> a 20 q tlo Wim lo 3 4 “) il