For a probability binomial distribution with P=0.50 and n=8 (a) Construct the probability distribution for all values of x (b) Graph the binomial distribution using a histogram
For a probability binomial distribution with P=0.50 and n=8 (a) Construct the probability distribution for all values of x (b) Graph the binomial distribution using a histogram
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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Question
![For a probability binomial distribution with \( P = 0.50 \) and \( n = 8 \):
(a) Construct the probability distribution for all values of \( x \).
(b) Graph the binomial distribution using a histogram.
---
### Explanation and Instructions:
1. **Probability Distribution Construction**:
- Calculate the probability \( P(X = x) \) using the binomial probability formula:
\[
P(X = x) = \binom{n}{x} P^x (1-P)^{n-x}
\]
- Here, \( \binom{n}{x} \) represents the binomial coefficient, \( n \) is the number of trials (8 in this case), \( x \) is the number of successful trials, and \( P \) is the probability of success on a single trial (0.50).
2. **Histogram of Binomial Distribution**:
- Plot the calculated probabilities on the y-axis against the corresponding values of \( x \) (ranging from 0 to 8) on the x-axis.
- Each bar in the histogram represents the probability of achieving exactly \( x \) successes out of 8 trials.
- The height of each bar indicates the likelihood of each outcome, showing the distribution of probabilities across different possible outcomes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7ee3c52-f428-4684-8136-b416ef58bd98%2Fe4852527-e1a0-43d4-be57-bd01dfeb52c3%2F7xf790l_processed.png&w=3840&q=75)
Transcribed Image Text:For a probability binomial distribution with \( P = 0.50 \) and \( n = 8 \):
(a) Construct the probability distribution for all values of \( x \).
(b) Graph the binomial distribution using a histogram.
---
### Explanation and Instructions:
1. **Probability Distribution Construction**:
- Calculate the probability \( P(X = x) \) using the binomial probability formula:
\[
P(X = x) = \binom{n}{x} P^x (1-P)^{n-x}
\]
- Here, \( \binom{n}{x} \) represents the binomial coefficient, \( n \) is the number of trials (8 in this case), \( x \) is the number of successful trials, and \( P \) is the probability of success on a single trial (0.50).
2. **Histogram of Binomial Distribution**:
- Plot the calculated probabilities on the y-axis against the corresponding values of \( x \) (ranging from 0 to 8) on the x-axis.
- Each bar in the histogram represents the probability of achieving exactly \( x \) successes out of 8 trials.
- The height of each bar indicates the likelihood of each outcome, showing the distribution of probabilities across different possible outcomes.
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