Problem 4) For the following random variable X [0 F₁(x)= 0.4 0.8 |1 a) Find the variance of the X. b) Find P(x), where the condition 8 = (X>0). c) Find EXIB). d) Find Var(XB). x<-3 -3≤x<5 5
Problem 4) For the following random variable X [0 F₁(x)= 0.4 0.8 |1 a) Find the variance of the X. b) Find P(x), where the condition 8 = (X>0). c) Find EXIB). d) Find Var(XB). x<-3 -3≤x<5 5
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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![**Problem 4**: For the following random variable \( X \)
\[
F_X(x) =
\begin{cases}
0 & \text{if } x < -3 \\
0.4 & \text{if } -3 \leq x < 5 \\
0.8 & \text{if } 5 \leq x < 7 \\
1 & \text{if } x \geq 7
\end{cases}
\]
a) Find the variance of \( X \).
b) Find \( P_{X|B}(x) \), where the condition \( B = \{X > 0\} \).
c) Find \( E[X|B] \).
d) Find \( \text{Var}[X|B] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2F3c1c25b4-2973-4a0b-be95-856a72ff20e9%2Fymuqpt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4**: For the following random variable \( X \)
\[
F_X(x) =
\begin{cases}
0 & \text{if } x < -3 \\
0.4 & \text{if } -3 \leq x < 5 \\
0.8 & \text{if } 5 \leq x < 7 \\
1 & \text{if } x \geq 7
\end{cases}
\]
a) Find the variance of \( X \).
b) Find \( P_{X|B}(x) \), where the condition \( B = \{X > 0\} \).
c) Find \( E[X|B] \).
d) Find \( \text{Var}[X|B] \).
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