The formula for finding the variance for a probability

Chapter 5, Problem 22EC

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QUESTION:

The formula for finding the variance for a probability distribution is

\(\sigma^{2}=\Sigma\left[(X-\mu)^{2} \cdot P(X)\right]\)

Verify algebraically that this formula gives the same result as the shortcut formula shown in this section.

Equation Transcription:

Text Transcription:

\sigma^{2}=\Sigma\left[(X-\mu)^{2} \cdot P(X)\right]

Questions & Answers

QUESTION:

The formula for finding the variance for a probability distribution is

\(\sigma^{2}=\Sigma\left[(X-\mu)^{2} \cdot P(X)\right]\)

Verify algebraically that this formula gives the same result as the shortcut formula shown in this section.

Equation Transcription:

Text Transcription:

\sigma^{2}=\Sigma\left[(X-\mu)^{2} \cdot P(X)\right]

ANSWER:

Solution 22EC

Step1 of 2:

From the given problem we have the formula for finding the variance for a probability distribution is:

We need to verify algebraically that this formula gives the same result as the shortcut formula shown in this section.


Step2 of 2:

We have,

The shortcut formula is:

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