A random variable is binomially distributed with n= 16 and T = 40. The expected value and standard deviation of the variables are Multiple Choice 2.00 and 1.24. 4.80 and 4.00. 6.40 and 1.96. 2.00 and 1.20.
A random variable is binomially distributed with n= 16 and T = 40. The expected value and standard deviation of the variables are Multiple Choice 2.00 and 1.24. 4.80 and 4.00. 6.40 and 1.96. 2.00 and 1.20.
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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![**Educational Website Content:**
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**Title: Understanding Binomial Distribution: Expected Value and Standard Deviation**
**Introduction:**
The binomial distribution is a widely used probability distribution in statistics. It models the number of successes in a fixed number of independent experiments, each with the same probability of success.
**Problem Statement:**
Given: A random variable is binomially distributed with parameters \( n = 16 \) and \( \pi = 0.40 \).
**Objective:**
Determine the expected value and standard deviation of the binomial distribution.
**Theory:**
- **Expected Value (Mean):** The expected value \( E(X) \) for a binomial distribution is calculated as:
\[
E(X) = n \cdot \pi
\]
- **Standard Deviation:** The standard deviation \( \sigma \) is calculated as:
\[
\sigma = \sqrt{n \cdot \pi \cdot (1 - \pi)}
\]
**Multiple Choice Options:**
Select the correct pair representing the expected value and standard deviation.
1. \( 2.00 \) and \( 1.24 \)
2. \( 4.80 \) and \( 4.00 \)
3. \( 6.40 \) and \( 1.96 \)
4. \( 2.00 \) and \( 1.20 \)
**Explanation:**
Based on the provided equations, plug in the values \( n = 16 \) and \( \pi = 0.40 \).
**Next Steps:**
After performing the calculations, compare your results with the given multiple-choice options to identify the correct answer.
---
**End of Content**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5b4bad2-60f3-49b7-8a7e-6feace3ebf44%2F3d6fe723-cb49-4569-af1e-ac7aca216240%2F75eka3d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content:**
---
**Title: Understanding Binomial Distribution: Expected Value and Standard Deviation**
**Introduction:**
The binomial distribution is a widely used probability distribution in statistics. It models the number of successes in a fixed number of independent experiments, each with the same probability of success.
**Problem Statement:**
Given: A random variable is binomially distributed with parameters \( n = 16 \) and \( \pi = 0.40 \).
**Objective:**
Determine the expected value and standard deviation of the binomial distribution.
**Theory:**
- **Expected Value (Mean):** The expected value \( E(X) \) for a binomial distribution is calculated as:
\[
E(X) = n \cdot \pi
\]
- **Standard Deviation:** The standard deviation \( \sigma \) is calculated as:
\[
\sigma = \sqrt{n \cdot \pi \cdot (1 - \pi)}
\]
**Multiple Choice Options:**
Select the correct pair representing the expected value and standard deviation.
1. \( 2.00 \) and \( 1.24 \)
2. \( 4.80 \) and \( 4.00 \)
3. \( 6.40 \) and \( 1.96 \)
4. \( 2.00 \) and \( 1.20 \)
**Explanation:**
Based on the provided equations, plug in the values \( n = 16 \) and \( \pi = 0.40 \).
**Next Steps:**
After performing the calculations, compare your results with the given multiple-choice options to identify the correct answer.
---
**End of Content**
Expert Solution
Step 1
Solution-:
Let, X=be the random variable with n=16 and p=0.40
Given:
We find, Mean and standard deviation
Step by step
Solved in 2 steps with 6 images
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