6.5. Let U ~ uniform(-1,1 so that X is a continuous random variable with pdf fu(u) 5 for %3D -1< u< 1; = 0 elsewhere. (a) Find the cdf Fy of U. This will be a piece-wise function so be sure to write it as such. (b) Consider the random variable Y = U³. Find the cdf Fy of Y. Again, it's piece-wise... (c) Use your answer to part (b) to derive the pdf fy (y) of Y.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question

""

please answer alll

6.5. Let U ~
uniform(-1,1), so that X is a continuous random variable with pdf fu(u)
I for
-1 < u< 1; = 0 elsewhere.
(a) Find the cdf Fy of U. This will be a piece-wise function so be sure to write it as such.
(b) Consider the random variable Y = U³. Find the cdf Fy of Y. Again, it's piece-wise...
(c) Use your answer to part (b) to derive the pdf fy (y) of Y.
(d,e) Repeat parts (b) and (c) when Y = U².
6.6. (continued from problem 6.5) (a) Compute E(U³) two ways: (i) by using the law of the uncon-
scious statistician, and (ii) by brute force by letting Y = U³ and computing E(Y) by the definition of
expectation.
(b) Repeat part (a) with E(U²).
Transcribed Image Text:6.5. Let U ~ uniform(-1,1), so that X is a continuous random variable with pdf fu(u) I for -1 < u< 1; = 0 elsewhere. (a) Find the cdf Fy of U. This will be a piece-wise function so be sure to write it as such. (b) Consider the random variable Y = U³. Find the cdf Fy of Y. Again, it's piece-wise... (c) Use your answer to part (b) to derive the pdf fy (y) of Y. (d,e) Repeat parts (b) and (c) when Y = U². 6.6. (continued from problem 6.5) (a) Compute E(U³) two ways: (i) by using the law of the uncon- scious statistician, and (ii) by brute force by letting Y = U³ and computing E(Y) by the definition of expectation. (b) Repeat part (a) with E(U²).
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman