(d) Evaluate f(x) by obtaining F'(x). f(x) = F'(x) = (e) Compute μ. 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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i need help with D) and E). plz dont mind zero in question E)
![The error involved in making a certain measurement is a continuous random variable \( X \) with the following cumulative distribution function (cdf):
\[
F(x) =
\begin{cases}
0 & x < -2 \\
\frac{1}{2} + \frac{3}{44}\left(5x - \frac{x^3}{3}\right) & -2 \leq x < 2 \\
1 & 2 \leq x
\end{cases}
\]
a) **Compute \( P(X < 0) \):**
The probability that \( X \) is less than 0 is 0.5.
b) **Compute \( P(-1 < X < 1) \):** (Round your answer to four decimal places.)
The probability that \( X \) falls between -1 and 1 is 0.6364.
c) **Compute \( P(0.4 < X) \):** (Round your answer to four decimal places.)
The probability that \( X \) is greater than 0.4 is 0.3651.
d) **Evaluate \( f(x) \) by obtaining \( F'(x) \):**
The derivative of \( F(x) \), which gives the probability density function \( f(x) \), is:
\[ f(x) = F'(x) = \]
e) **Compute \(\tilde{\mu}\):**
The expected value \(\tilde{\mu}\) is 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4927fb7d-fe4d-496e-94ae-b9c9f1ed73cb%2F08b9abfb-13f6-45c8-8d4e-4b059843ae06%2F23wi9ze_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The error involved in making a certain measurement is a continuous random variable \( X \) with the following cumulative distribution function (cdf):
\[
F(x) =
\begin{cases}
0 & x < -2 \\
\frac{1}{2} + \frac{3}{44}\left(5x - \frac{x^3}{3}\right) & -2 \leq x < 2 \\
1 & 2 \leq x
\end{cases}
\]
a) **Compute \( P(X < 0) \):**
The probability that \( X \) is less than 0 is 0.5.
b) **Compute \( P(-1 < X < 1) \):** (Round your answer to four decimal places.)
The probability that \( X \) falls between -1 and 1 is 0.6364.
c) **Compute \( P(0.4 < X) \):** (Round your answer to four decimal places.)
The probability that \( X \) is greater than 0.4 is 0.3651.
d) **Evaluate \( f(x) \) by obtaining \( F'(x) \):**
The derivative of \( F(x) \), which gives the probability density function \( f(x) \), is:
\[ f(x) = F'(x) = \]
e) **Compute \(\tilde{\mu}\):**
The expected value \(\tilde{\mu}\) is 0.
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