2. The cumulative distribution function of random variable X is , х> 1 Kx Fx (x) = ,0 < x< 1 x2 + 1 , х < 0 (a) Find K. (b) Find the p.d.f fx(x). (c) The random variable Y is the output of the clipper: 1 ,X 2 1 1 Y = {0.5 2 ,0 < X < -1 4 What is E{Y}? VI

2. The cumulative distribution function of random variable X is , х> 1 Kx Fx (x) = ,0 < x< 1 x2 + 1 , х < 0 (a) Find K. (b) Find the p.d.f fx(x). (c) The random variable Y is the output of the clipper: 1 ,X 2 1 1 Y = {0.5 2 ,0 < X < -1 4 What is E{Y}? VI

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

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Question

2. The cumulative distribution function of random variable X is
1
,x > 1
Kx
Fx(x)
,0 < x < 1
x2 + 1
,x < 0
(a) Find K.
(b) Find the p.d.f fx(x).
(c) The random variable Y is the output of the clipper:
1
,X
2
1
1
Y = { 0.5
2
1
,0 < X <-
-1
4
What is E{Y}?
(d) Find the characteristic function of Y. (Øy(w) =?)
Hint: Y can be considered as a discrete r.v.

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