Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 0, 2, 4, 5, and 6. Value x of X P(X = x) 2 0.26 4. 0.30 5 0.11 6
Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 0, 2, 4, 5, and 6. Value x of X P(X = x) 2 0.26 4. 0.30 5 0.11 6
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Question
![To complete the probability distribution for the discrete random variable \(X\), fill in the values of \(P(X = x)\) such that they sum to 1. The possible values of \(X\) are 0, 2, 4, 5, and 6.
Here is the given table with the probabilities provided:
| Value \(x\) of \(X\) | \(P(X = x)\) |
|----------------------|------------|
| 0 | \(\_\_\_\_) |
| 2 | 0.26 |
| 4 | 0.30 |
| 5 | 0.11 |
| 6 | \(\_\_\_\_) |
To find a legitimate probability distribution:
1. The sum of all probabilities must equal 1:
\[
P(X=0) + 0.26 + 0.30 + 0.11 + P(X=6) = 1
\]
2. Calculate the missing probabilities for \(P(X=0)\) and \(P(X=6)\) to satisfy the equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe17a999b-a7db-49d7-b1d3-602b036c3370%2Fb99c1e1e-de22-41af-8030-cce42517adcf%2Fj7uy2r_processed.png&w=3840&q=75)
Transcribed Image Text:To complete the probability distribution for the discrete random variable \(X\), fill in the values of \(P(X = x)\) such that they sum to 1. The possible values of \(X\) are 0, 2, 4, 5, and 6.
Here is the given table with the probabilities provided:
| Value \(x\) of \(X\) | \(P(X = x)\) |
|----------------------|------------|
| 0 | \(\_\_\_\_) |
| 2 | 0.26 |
| 4 | 0.30 |
| 5 | 0.11 |
| 6 | \(\_\_\_\_) |
To find a legitimate probability distribution:
1. The sum of all probabilities must equal 1:
\[
P(X=0) + 0.26 + 0.30 + 0.11 + P(X=6) = 1
\]
2. Calculate the missing probabilities for \(P(X=0)\) and \(P(X=6)\) to satisfy the equation.
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