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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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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 42E

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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.

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