Problem 3) Let X have the binomial PMF P. (x)-()* = a) Find the standard deviation of the random variable X. b) What is P[ux - Ox ≤ x ≤ µx + ox], the probability that X is within one standard deviation of the expected value. e) Find PX/B(x), where the condition B = {X # 0}. f) Find E[X|B]. g) Find Var[X|B].
Problem 3) Let X have the binomial PMF P. (x)-()* = a) Find the standard deviation of the random variable X. b) What is P[ux - Ox ≤ x ≤ µx + ox], the probability that X is within one standard deviation of the expected value. e) Find PX/B(x), where the condition B = {X # 0}. f) Find E[X|B]. g) Find Var[X|B].
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 3** Let \( X \) have the binomial PMF
\[
P_X(x) = \binom{4}{x} \left(\frac{1}{2}\right)^4
\]
a) Find the standard deviation of the random variable \( X \).
b) What is \( P[\mu_X - \sigma_X \leq X \leq \mu_X + \sigma_X] \), the probability that \( X \) is within one standard deviation of the expected value.
e) Find \( P_{X|B}(x) \), where the condition \( B = \{X \neq 0\} \).
f) Find \( E[X|B] \).
g) Find \( \text{Var}[X|B] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2F017a8e7d-ab43-4716-862e-a16c8395cdda%2Fd3ey0b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3** Let \( X \) have the binomial PMF
\[
P_X(x) = \binom{4}{x} \left(\frac{1}{2}\right)^4
\]
a) Find the standard deviation of the random variable \( X \).
b) What is \( P[\mu_X - \sigma_X \leq X \leq \mu_X + \sigma_X] \), the probability that \( X \) is within one standard deviation of the expected value.
e) Find \( P_{X|B}(x) \), where the condition \( B = \{X \neq 0\} \).
f) Find \( E[X|B] \).
g) Find \( \text{Var}[X|B] \).
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