Ifa is a binomial random variable, compute P(x) for each of the following cases: (a) P(x ≤ 4), n = 6, p = 0.4 P(x) = (b) P(x > 3), n = 9, p = 0.3 P(x) = (c) P(x <3), n = 4, p=0.6 P(x) = (d) P(x ≥ 4), n = 8, p = 0.2 P(x): op
Ifa is a binomial random variable, compute P(x) for each of the following cases: (a) P(x ≤ 4), n = 6, p = 0.4 P(x) = (b) P(x > 3), n = 9, p = 0.3 P(x) = (c) P(x <3), n = 4, p=0.6 P(x) = (d) P(x ≥ 4), n = 8, p = 0.2 P(x): op
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 Random Variable Computation
If \( x \) is a binomial random variable, compute \( P(x) \) for each of the following cases:
#### (a) \( P(x \leq 4) \), \( n = 6 \), \( p = 0.4 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
#### (b) \( P(x \geq 3) \), \( n = 9 \), \( p = 0.3 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
#### (c) \( P(x < 3) \), \( n = 4 \), \( p = 0.6 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
#### (d) \( P(x \geq 4) \), \( n = 8 \), \( p = 0.2 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
---
**Explanation of Terms and Symbols:**
- **\( x \)**: The number of successes in \( n \) trials.
- **\( n \)**: The number of trials.
- **\( p \)**: The probability of success on an individual trial.
- **\( P(x) \)**: The probability of \( x \) successes in \( n \) trials.
**Note:** The probabilities can be calculated using the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
where
\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]
To solve for probabilities across a range of values (e.g., \( x \leq y \) or \( x \geq z \)), you would sum the individual probabilities for the relevant values of \( x \).
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Transcribed Image Text:---
### Binomial Random Variable Computation
If \( x \) is a binomial random variable, compute \( P(x) \) for each of the following cases:
#### (a) \( P(x \leq 4) \), \( n = 6 \), \( p = 0.4 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
#### (b) \( P(x \geq 3) \), \( n = 9 \), \( p = 0.3 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
#### (c) \( P(x < 3) \), \( n = 4 \), \( p = 0.6 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
#### (d) \( P(x \geq 4) \), \( n = 8 \), \( p = 0.2 \)
\[
P(x) = \_\_\_\_\_\_\_
\]
---
**Explanation of Terms and Symbols:**
- **\( x \)**: The number of successes in \( n \) trials.
- **\( n \)**: The number of trials.
- **\( p \)**: The probability of success on an individual trial.
- **\( P(x) \)**: The probability of \( x \) successes in \( n \) trials.
**Note:** The probabilities can be calculated using the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
where
\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]
To solve for probabilities across a range of values (e.g., \( x \leq y \) or \( x \geq z \)), you would sum the individual probabilities for the relevant values of \( x \).
---
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