**Understanding Binomial Distributions: Expected Mean Calculation***Problem Statement:*"Assume you have a binomial distribution. In an experiment with 100 trials and a probability of a success equal to one half, what is the mean?"*Explanation:*In a binomial distribution, the mean (expected value) can be determined using the formula:\[ \text{Mean} (\mu) = n \cdot p \]where:- $ n $ = number of trials- $ p $ = probability of success on a single trialFor this specific problem:- Number of trials ($ n $) = 100- Probability of success on a single trial ($ p $) = 0.5Plugging in the values:\[ \mu = 100 \cdot 0.5 \]\[ \mu = 50 \]Hence, the mean for this binomial distribution is 50.This example is useful in understanding binomial distributions, which frequently arise in practical statistical problems.

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Assume you have a binomial distribution. In an experiment with 100 trials and a probability of a success equal to one half, what is the mean?

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Understanding Binomial Distributions: Expected Mean Calculation**

*Problem Statement:*
"Assume you have a binomial distribution. In an experiment with 100 trials and a probability of a success equal to one half, what is the mean?"

*Explanation:*
In a binomial distribution, the mean (expected value) can be determined using the formula:
\[ \text{Mean} (\mu) = n \cdot p \]
where:
- $ n $ = number of trials
- $ p $ = probability of success on a single trial

For this specific problem:
- Number of trials ($ n $) = 100
- Probability of success on a single trial ($ p $) = 0.5

Plugging in the values:
\[ \mu = 100 \cdot 0.5 \]
\[ \mu = 50 \]

Hence, the mean for this binomial distribution is 50.

This example is useful in understanding binomial distributions, which frequently arise in practical statistical problems.

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