in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, -1, 1, 5, and 6. P ( X = x) Value x of X Check -3 -1 1 5 6 X 0.20 0.15 0 0.28 S M 31 Save For Later © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center Accessi Submit Assignme

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The task involves filling in the \( P(X = x) \) values to create a legitimate probability distribution for a discrete random variable \( X \), with possible values of \(-3\), \(-1\), \(1\), \(5\), and \(6\).

### Probability Distribution Table

| Value \( x \) of \( X \) | \( P(X = x) \) |
|--------------------------|----------------|
| \(-3\)                   | \(0.20\)       |
| \(-1\)                   | \(0.15\)       |
| \(1\)                    | \([ \, ? \, ]\)|
| \(5\)                    | \(0.28\)       |
| \(6\)                    | \([ \, ? \, ]\)|

### Explanation

To ensure a legitimate probability distribution:

1. All probabilities \( P(X = x) \) must be non-negative.
2. The sum of the probabilities must equal 1.

Currently, the known probabilities are: 

\[
0.20 + 0.15 + 0.28 = 0.63
\]

The sum of the unknown probabilities for \( X = 1 \) and \( X = 6 \) should be \(1 - 0.63 = 0.37\). 

You can distribute these probabilities to complete the table. Adjust the values of \( P(X = 1) \) and \( P(X = 6) \) to sum to 0.37 while ensuring all conditions for the probability distribution are met.
Transcribed Image Text:The task involves filling in the \( P(X = x) \) values to create a legitimate probability distribution for a discrete random variable \( X \), with possible values of \(-3\), \(-1\), \(1\), \(5\), and \(6\). ### Probability Distribution Table | Value \( x \) of \( X \) | \( P(X = x) \) | |--------------------------|----------------| | \(-3\) | \(0.20\) | | \(-1\) | \(0.15\) | | \(1\) | \([ \, ? \, ]\)| | \(5\) | \(0.28\) | | \(6\) | \([ \, ? \, ]\)| ### Explanation To ensure a legitimate probability distribution: 1. All probabilities \( P(X = x) \) must be non-negative. 2. The sum of the probabilities must equal 1. Currently, the known probabilities are: \[ 0.20 + 0.15 + 0.28 = 0.63 \] The sum of the unknown probabilities for \( X = 1 \) and \( X = 6 \) should be \(1 - 0.63 = 0.37\). You can distribute these probabilities to complete the table. Adjust the values of \( P(X = 1) \) and \( P(X = 6) \) to sum to 0.37 while ensuring all conditions for the probability distribution are met.
Expert Solution
Step 1: Introduce the given information

Here the given probability distribution table is:-

Statistics homework question answer, step 1, image 1

We have to complete the missing values of the table .

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