Consider the probability distribution: X P(X) 0 3 a. What is the missing value, p? b. Draw a bar graph for the probability distribution.
Consider the probability distribution: X P(X) 0 3 a. What is the missing value, p? b. Draw a bar graph for the probability distribution.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 20E
Related questions
Question
![7. Consider the probability distribution:
| X | 0 | 1 | 2 | 3 |
|-----|----|----|----|----|
| P(X)| .3 | .2 | p | .4 |
a. What is the missing value, \( p \)?
b. Draw a bar graph for the probability distribution.
**Explanation:**
To find the missing value \( p \), remember that the sum of all probabilities in a distribution must equal 1. Therefore,
\[
0.3 + 0.2 + p + 0.4 = 1
\]
This simplifies to
\[
p = 1 - 0.9 = 0.1
\]
**Bar Graph Description:**
- The x-axis of the bar graph represents the random variable \( X \) with values 0, 1, 2, and 3.
- The y-axis represents the probability \( P(X) \).
- Each value of \( X \) has a corresponding bar:
- For \( X = 0 \), the height of the bar is 0.3.
- For \( X = 1 \), the height of the bar is 0.2.
- For \( X = 2 \), the height of the bar is 0.1.
- For \( X = 3 \), the height of the bar is 0.4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8033e12-306b-4455-b62f-c75f6c572a50%2Fd5e1a01e-deb9-4ab9-a0c9-ba3c8a8dfad1%2F7j8gp6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Consider the probability distribution:
| X | 0 | 1 | 2 | 3 |
|-----|----|----|----|----|
| P(X)| .3 | .2 | p | .4 |
a. What is the missing value, \( p \)?
b. Draw a bar graph for the probability distribution.
**Explanation:**
To find the missing value \( p \), remember that the sum of all probabilities in a distribution must equal 1. Therefore,
\[
0.3 + 0.2 + p + 0.4 = 1
\]
This simplifies to
\[
p = 1 - 0.9 = 0.1
\]
**Bar Graph Description:**
- The x-axis of the bar graph represents the random variable \( X \) with values 0, 1, 2, and 3.
- The y-axis represents the probability \( P(X) \).
- Each value of \( X \) has a corresponding bar:
- For \( X = 0 \), the height of the bar is 0.3.
- For \( X = 1 \), the height of the bar is 0.2.
- For \( X = 2 \), the height of the bar is 0.1.
- For \( X = 3 \), the height of the bar is 0.4.
Expert Solution
Step 1: We have given that
Probability mass function of X is
| x | 0 | 1 | 2 | 3 |
| P(x) | 0.3 | 0.2 | p | 0.4 |
Step by step
Solved in 3 steps with 1 images
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