Suppose there is a random variable X whose probability density function has the form (shown in image). a) Find P(X>-0.2) b) Find the 90th percentile
Suppose there is a random variable X whose probability density function has the form (shown in image). a) Find P(X>-0.2) b) Find the 90th percentile
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
Suppose there is a random variable X whose probability density
a) Find P(X>-0.2)
b) Find the 90th percentile
![The piecewise function \( f(x) \) is defined as follows:
\[
f(x) =
\begin{cases}
1 + x, & \text{if } -1 \leq x < 0 \\
1 - x, & \text{if } 0 \leq x < 1 \\
0, & \text{otherwise.}
\end{cases}
\]
This piecewise function specifies different expressions for different intervals of \( x \). Here's a breakdown of each part:
- For values of \( x \) between \(-1\) and \(0\) (inclusive of \(-1\) and exclusive of \(0\)), the function is defined as \( f(x) = 1 + x \).
- For values of \( x \) between \(0\) and \(1\) (inclusive of \(0\) and exclusive of \(1\)), the function is \( f(x) = 1 - x \).
- For values of \( x \) outside the interval \([-1, 1)\), the function is \( f(x) = 0 \).
This function is commonly used in mathematical contexts to represent different behaviors over specified domains.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff490fc5e-f29e-4ef4-a7f0-8835aa77e897%2F09dc2270-b9de-4f94-a95a-4776047cd8f0%2Fwoaxmos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The piecewise function \( f(x) \) is defined as follows:
\[
f(x) =
\begin{cases}
1 + x, & \text{if } -1 \leq x < 0 \\
1 - x, & \text{if } 0 \leq x < 1 \\
0, & \text{otherwise.}
\end{cases}
\]
This piecewise function specifies different expressions for different intervals of \( x \). Here's a breakdown of each part:
- For values of \( x \) between \(-1\) and \(0\) (inclusive of \(-1\) and exclusive of \(0\)), the function is defined as \( f(x) = 1 + x \).
- For values of \( x \) between \(0\) and \(1\) (inclusive of \(0\) and exclusive of \(1\)), the function is \( f(x) = 1 - x \).
- For values of \( x \) outside the interval \([-1, 1)\), the function is \( f(x) = 0 \).
This function is commonly used in mathematical contexts to represent different behaviors over specified domains.
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