If a random variable X with the following distribution has mean value of 0.6, find 2 3 0.1 x P(X=x) a) the value of m and the value of n b) P(X<=1) c) variance of X d) expected value of Y=3X+1 e) variance of Y=3X+1 -1 0 m n 1 0.2 0.2
If a random variable X with the following distribution has mean value of 0.6, find 2 3 0.1 x P(X=x) a) the value of m and the value of n b) P(X<=1) c) variance of X d) expected value of Y=3X+1 e) variance of Y=3X+1 -1 0 m n 1 0.2 0.2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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Please help on parts c, d, and e.
![**Problem: Probability Distribution and Random Variables**
If a random variable \( X \) with the following distribution has a mean value of 0.6, find:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 & 3 \\
\hline
P(X=x) & m & n & 0.2 & 0.1 & 0.2 \\
\hline
\end{array}
\]
**Questions:**
a) Determine the values of \( m \) and \( n \).
b) Calculate \( P(X \leq 1) \).
c) Find the variance of \( X \).
d) Compute the expected value of \( Y = 3X + 1 \).
e) Determine the variance of \( Y = 3X + 1 \).
**Instructions:**
1. Use the definition of the mean (expected value) to find \( m \) and \( n \).
2. Use the probability rules to compute \( P(X \leq 1) \).
3. Apply the formula for variance to find the variance of \( X \).
4. Use properties of expectation and linear transformations to find the expected value of \( Y \).
5. Use properties of variance under linear transformations to find the variance of \( Y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3311208f-e111-4329-929a-ce99cbd4dfb6%2F1cf1356d-9f43-43b3-bb3f-fbcff067671b%2Fdtl8nq_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Probability Distribution and Random Variables**
If a random variable \( X \) with the following distribution has a mean value of 0.6, find:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 & 3 \\
\hline
P(X=x) & m & n & 0.2 & 0.1 & 0.2 \\
\hline
\end{array}
\]
**Questions:**
a) Determine the values of \( m \) and \( n \).
b) Calculate \( P(X \leq 1) \).
c) Find the variance of \( X \).
d) Compute the expected value of \( Y = 3X + 1 \).
e) Determine the variance of \( Y = 3X + 1 \).
**Instructions:**
1. Use the definition of the mean (expected value) to find \( m \) and \( n \).
2. Use the probability rules to compute \( P(X \leq 1) \).
3. Apply the formula for variance to find the variance of \( X \).
4. Use properties of expectation and linear transformations to find the expected value of \( Y \).
5. Use properties of variance under linear transformations to find the variance of \( Y \).
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