4.8 Mean and Standard Deviation of Random Variables

Part of Probability, Random Variables, and Probability Distributions in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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Expected Value (Mean)

The expected value

\mu_X = E(X) = \sum_x x \cdot P(X = x)

Interpretation: If the experiment is repeated many times, the average value of X approaches ${\mu_X}$ .

Example: Insurance company sells policies. Each year:

1 in 1000 customers makes a $50,000 claim
5 in 1000 make a $10,000 claim
The rest make no claim

${\mu_X = 50000(0.001) + 10000(0.005) + 0(0.994) = 50 + 50 + 0 = \$100}$

The company needs to charge more than $100 per policy to be profitable.

Properties of Expected Value:

${E(aX + b) = a \cdot E(X) + b}$ (linear transformation)
${E(X + Y) = E(X) + E(Y)}$ (for any X and Y)

In this unit

12 lessons

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