Answered: (a) The continuous random variables X… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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please send solution for part a I amd ii

Question 4
(a) The continuous random variables X and Y are distributed uniformly on (0, 1)
and exponentially with mean 1, respectively. X and Y are independent.
(i) Use the convolution formula to show that the random variable Z = X +Y
has probability density function (pdf)
= (2)25
(e - 1) e-, z> 1.
1-e=²,
0 <z<%;
(ii) Show that fz(z) is a valid pdf.
(iii) Let Fz(z) be the cumulative distribution function (cdf) of Z. Show that
z<0;
0,
z+e-1,
Fz(2)
0<z<1;
%3D
e(1- e) +1, z> 1.
and hence find the median of Z.
(b) The random variable X has pdf
S 6x (1-2), 0 < x < 1;
otherwise.
fx (x) =
Determine the pdf of Y = X/(1 X).
(c) The random variable X has pdf

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