The probability density function (pdf) of continuous random variable X is as follows: x<0 0

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
Question
The probability density function (pdf) of continuous random variable X is as follows:

\[ 
f(x) = 
\begin{cases} 
0 & x \leq 0 \\
x^2 & 0 \leq x \leq 1 \\
\frac{4x}{9} & 1 \leq x \leq 2 \\
0 & x \geq 2 \\
\end{cases} 
\]

Tasks:
a. Determine the cumulative density function (cdf) of the random variable X.

b. Compute the probability that X is less than or equal to 0.5.

c. Compute the probability that X is greater than or equal to 1.5.

d. Compute the probability that X is between 0.5 and 1.5.
Transcribed Image Text:The probability density function (pdf) of continuous random variable X is as follows: \[ f(x) = \begin{cases} 0 & x \leq 0 \\ x^2 & 0 \leq x \leq 1 \\ \frac{4x}{9} & 1 \leq x \leq 2 \\ 0 & x \geq 2 \\ \end{cases} \] Tasks: a. Determine the cumulative density function (cdf) of the random variable X. b. Compute the probability that X is less than or equal to 0.5. c. Compute the probability that X is greater than or equal to 1.5. d. Compute the probability that X is between 0.5 and 1.5.
Expert Solution
Step 1

Statistics homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

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