The probability density function (pdf) of continuous random variable X is as follows: x<0 0
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
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd65464ea-20ac-437a-9b4f-902b3affc00d%2Fde9b43fd-5215-4a76-80d7-55ef86efbfa1%2Fr6pjc5f_processed.jpeg&w=3840&q=75)
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.
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