MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
Please help on parts c, d, and e.
![**Problem: Probability Distribution and Random Variables**
If a random variable \( X \) with the following distribution has a mean value of 0.6, find:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 & 3 \\
\hline
P(X=x) & m & n & 0.2 & 0.1 & 0.2 \\
\hline
\end{array}
\]
**Questions:**
a) Determine the values of \( m \) and \( n \).
b) Calculate \( P(X \leq 1) \).
c) Find the variance of \( X \).
d) Compute the expected value of \( Y = 3X + 1 \).
e) Determine the variance of \( Y = 3X + 1 \).
**Instructions:**
1. Use the definition of the mean (expected value) to find \( m \) and \( n \).
2. Use the probability rules to compute \( P(X \leq 1) \).
3. Apply the formula for variance to find the variance of \( X \).
4. Use properties of expectation and linear transformations to find the expected value of \( Y \).
5. Use properties of variance under linear transformations to find the variance of \( Y \).](https://content.bartleby.com/qna-images/question/3311208f-e111-4329-929a-ce99cbd4dfb6/1cf1356d-9f43-43b3-bb3f-fbcff067671b/dtl8nq_processed.png)
Transcribed Image Text:**Problem: Probability Distribution and Random Variables**
If a random variable \( X \) with the following distribution has a mean value of 0.6, find:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 & 3 \\
\hline
P(X=x) & m & n & 0.2 & 0.1 & 0.2 \\
\hline
\end{array}
\]
**Questions:**
a) Determine the values of \( m \) and \( n \).
b) Calculate \( P(X \leq 1) \).
c) Find the variance of \( X \).
d) Compute the expected value of \( Y = 3X + 1 \).
e) Determine the variance of \( Y = 3X + 1 \).
**Instructions:**
1. Use the definition of the mean (expected value) to find \( m \) and \( n \).
2. Use the probability rules to compute \( P(X \leq 1) \).
3. Apply the formula for variance to find the variance of \( X \).
4. Use properties of expectation and linear transformations to find the expected value of \( Y \).
5. Use properties of variance under linear transformations to find the variance of \( Y \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 2 images
Knowledge Booster
Similar questions
- How did you get the figures for the calculations in part d for Question 4?arrow_forward1 D A F B G E 2 с a. Give another name for BC.arrow_forwardQuestion 3. To ship a box with USPS, the sum of the length, width, and height cannot exceed 108 inches. Suppose you are shipping a rectangular box with a square base. What is the largest volume your box can have, and what dimensions yield that volume?arrow_forward
- Question 4 Your neighbor is digging a hole in his back yard for an in-ground swimming pool. The rectangular hole is 7 meters wide, 14 meters long, and 4 meters deep. If his pickup truck can haul one cubic meter, how many trips will it take him to haul all of the dirt away? O 10,584 O 3,528 Ⓒ 392 O 44arrow_forwardstem. leaf 3 0 0 1 1 2 4 5 6 9 4 1 5 5 6 5 6 7 7 6 0 1 7 8 9 9 describe shape center peaks and spread.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
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
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
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
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman