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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
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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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.
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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