P(X ≤ 1). n = 5, p = 0.6
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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![### Binomial Probability Calculation
**Given:**
- \(P(X \leq 1)\)
- \(n = 5\)
- \(p = 0.6\)
This mathematical expression represents the cumulative probability in a binomial distribution.
- **\(P(X \leq 1)\)**: This indicates the probability that the random variable \(X\) is less than or equal to 1.
- **\(n = 5\)**: This represents the number of trials or experiments.
- **\(p = 0.6\)**: This denotes the probability of success in each trial.
In the context of a binomial distribution, we are interested in finding the probability that \(X\), the number of successes in 5 trials, is at most 1 when the probability of success in each trial is 0.6.
To calculate this cumulative probability, we typically use the binomial probability formula or statistical software/table:
\[ P(X \leq 1) = \sum_{k=0}^{1} {P(X = k)} \]
where:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Here, \(\binom{n}{k}\) is the binomial coefficient.
The probability values can be summed up for \(k = 0\) and \(k = 1\):
\[ P(X \leq 1) = P(X = 0) + P(X = 1) \]
By calculating each individual term, one can find the cumulative probability for \(X \leq 1\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F786a2b18-36fc-4a59-90dc-399df5403cec%2F9c540cbe-c64d-4d53-837c-a8234296b271%2Fki7iccf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Binomial Probability Calculation
**Given:**
- \(P(X \leq 1)\)
- \(n = 5\)
- \(p = 0.6\)
This mathematical expression represents the cumulative probability in a binomial distribution.
- **\(P(X \leq 1)\)**: This indicates the probability that the random variable \(X\) is less than or equal to 1.
- **\(n = 5\)**: This represents the number of trials or experiments.
- **\(p = 0.6\)**: This denotes the probability of success in each trial.
In the context of a binomial distribution, we are interested in finding the probability that \(X\), the number of successes in 5 trials, is at most 1 when the probability of success in each trial is 0.6.
To calculate this cumulative probability, we typically use the binomial probability formula or statistical software/table:
\[ P(X \leq 1) = \sum_{k=0}^{1} {P(X = k)} \]
where:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Here, \(\binom{n}{k}\) is the binomial coefficient.
The probability values can be summed up for \(k = 0\) and \(k = 1\):
\[ P(X \leq 1) = P(X = 0) + P(X = 1) \]
By calculating each individual term, one can find the cumulative probability for \(X \leq 1\).
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