If X is a binomial random variable, compute the following probabilities: a) n = 4, p = 0.5 P(X ≤ 1) = 0.3125 b) n = 7, p = 0.2 P(X> 4) = 0.08315136 c) n = 9, p = 0.8 P(X<5)= 0.938457216
If X is a binomial random variable, compute the following probabilities: a) n = 4, p = 0.5 P(X ≤ 1) = 0.3125 b) n = 7, p = 0.2 P(X> 4) = 0.08315136 c) n = 9, p = 0.8 P(X<5)= 0.938457216
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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![### Computing Binomial Probabilities
If \( X \) is a binomial random variable, compute the following probabilities:
a) For \( n = 4 \) and \( p = 0.5 \):
\[
P(X \leq 1) = 0.3125
\]
b) For \( n = 7 \) and \( p = 0.2 \):
\[
P(X > 4) = 0.08315136
\]
c) For \( n = 9 \) and \( p = 0.8 \):
\[
P(X < 5) = 0.938457216
\]
d) For \( n = 4 \) and \( p = 0.9 \):
\[
P(X \geq 2) = 0.9963
\]
For each calculation:
- \( n \) is the number of trials.
- \( p \) is the probability of success on a single trial.
- \( X \) represents the number of successes in \( n \) trials.
These probabilities are computed using the properties of the binomial distribution:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
where \(\binom{n}{k}\) is the binomial coefficient.
The exact values are generally found using statistical software or binomial probability tables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5386f0c-0c7d-4f0c-9c77-b0195c82b8c2%2F9e0082df-8fc1-4dae-8ba3-338273ceab8f%2Fhbi3lcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Computing Binomial Probabilities
If \( X \) is a binomial random variable, compute the following probabilities:
a) For \( n = 4 \) and \( p = 0.5 \):
\[
P(X \leq 1) = 0.3125
\]
b) For \( n = 7 \) and \( p = 0.2 \):
\[
P(X > 4) = 0.08315136
\]
c) For \( n = 9 \) and \( p = 0.8 \):
\[
P(X < 5) = 0.938457216
\]
d) For \( n = 4 \) and \( p = 0.9 \):
\[
P(X \geq 2) = 0.9963
\]
For each calculation:
- \( n \) is the number of trials.
- \( p \) is the probability of success on a single trial.
- \( X \) represents the number of successes in \( n \) trials.
These probabilities are computed using the properties of the binomial distribution:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
where \(\binom{n}{k}\) is the binomial coefficient.
The exact values are generally found using statistical software or binomial probability tables.
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