Homework Help is Here – Start Your Trial Now!
Math
Statistics
(a) Determine the pmf of T, = X1 + X2. to 1 3 4 p(t,) ||0.16 0.24 0.33

(a) Determine the pmf of T, = X1 + X2. to 1 3 4 p(t,) ||0.16 0.24 0.33

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

There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2).

 

Can you help me with 3 and 4?

### Discrete Probability Distribution #### Given Probability Distribution for \( X_1 \) - **Values of \( x_1 \):** 0, 1, 2 - **Probability \( p(x_1) \):** - \( P(x_1 = 0) = 0.4 \) - \( P(x_1 = 1) = 0.3 \) - \( P(x_1 = 2) = 0.3 \) **Mean (\( \mu \)) and Variance (\( \sigma^2 \))**: - \( \mu = 0.9 \) - \( \sigma^2 = 0.69 \) #### Task (a) Determine the probability mass function (pmf) of \( T_0 = X_1 + X_2 \). #### Probability Distribution for \( T_0 \) - **Values of \( t_0 \):** 0, 1, 2, 3, 4 - **Probability \( p(t_0) \):** - \( P(t_0 = 0) = 0.16 \) ✔️ - \( P(t_0 = 1) = 0.24 \) ✔️ - \( P(t_0 = 2) = 0.33 \) ✔️ #### Explanation In the given distributions, the probabilities for \( t_0 = 0 \), \( t_0 = 1 \), and \( t_0 = 2 \) are specified with check marks, indicating these values are confirmed. Additional probability values for \( t_0 = 3 \) and \( t_0 = 4 \) need to be determined to complete the distribution.
Transcribed Image Text:### Discrete Probability Distribution #### Given Probability Distribution for \( X_1 \) - **Values of \( x_1 \):** 0, 1, 2 - **Probability \( p(x_1) \):** - \( P(x_1 = 0) = 0.4 \) - \( P(x_1 = 1) = 0.3 \) - \( P(x_1 = 2) = 0.3 \) **Mean (\( \mu \)) and Variance (\( \sigma^2 \))**: - \( \mu = 0.9 \) - \( \sigma^2 = 0.69 \) #### Task (a) Determine the probability mass function (pmf) of \( T_0 = X_1 + X_2 \). #### Probability Distribution for \( T_0 \) - **Values of \( t_0 \):** 0, 1, 2, 3, 4 - **Probability \( p(t_0) \):** - \( P(t_0 = 0) = 0.16 \) ✔️ - \( P(t_0 = 1) = 0.24 \) ✔️ - \( P(t_0 = 2) = 0.33 \) ✔️ #### Explanation In the given distributions, the probabilities for \( t_0 = 0 \), \( t_0 = 1 \), and \( t_0 = 2 \) are specified with check marks, indicating these values are confirmed. Additional probability values for \( t_0 = 3 \) and \( t_0 = 4 \) need to be determined to complete the distribution.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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
SEE MORE TEXTBOOKS