Evaluate the cumulative distribution function of a binomial random variable with n = 3 and p = 1/7 at specified points. Give exact answers in form of fraction. F(0) = F(1) = F(2) = F(3) = i
Evaluate the cumulative distribution function of a binomial random variable with n = 3 and p = 1/7 at specified points. Give exact answers in form of fraction. F(0) = F(1) = F(2) = F(3) = i
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Understanding the Cumulative Distribution Function for Binomial Distribution**
Evaluate the cumulative distribution function of a binomial random variable with \( n = 3 \) and \( p = \frac{1}{7} \) at specified points.
**Give exact answers in fraction form**:
\[ F(0) = \] [Input Box]
\[ F(1) = \] [Input Box]
\[ F(2) = \] [Input Box]
\[ F(3) = \] [Input Box with Information Icon]
### Explanation
In this problem, you are required to find the cumulative distribution function (CDF) of a binomial random variable at specific points. The parameters given are:
- \( n = 3 \): This indicates that the number of trials is 3.
- \( p = \frac{1}{7} \): This is the probability of success in a single trial.
For each value \( k \) (0 through 3), the CDF, \( F(k) \), is the probability that the binomial random variable is less than or equal to \( k \). The exact answers should be provided in the form of a fraction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F548b861a-42f3-4cfc-8e03-f464d56fea49%2F0752c22a-71bc-4fdc-affd-e7d2ad9a50b3%2Fryruody_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding the Cumulative Distribution Function for Binomial Distribution**
Evaluate the cumulative distribution function of a binomial random variable with \( n = 3 \) and \( p = \frac{1}{7} \) at specified points.
**Give exact answers in fraction form**:
\[ F(0) = \] [Input Box]
\[ F(1) = \] [Input Box]
\[ F(2) = \] [Input Box]
\[ F(3) = \] [Input Box with Information Icon]
### Explanation
In this problem, you are required to find the cumulative distribution function (CDF) of a binomial random variable at specific points. The parameters given are:
- \( n = 3 \): This indicates that the number of trials is 3.
- \( p = \frac{1}{7} \): This is the probability of success in a single trial.
For each value \( k \) (0 through 3), the CDF, \( F(k) \), is the probability that the binomial random variable is less than or equal to \( k \). The exact answers should be provided in the form of a fraction.
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