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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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.
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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