Back to Calculate the expected value of a random variable — Problem 5 · Task Set 28

Exercises: Calculate the Expected Value of a Random Variable

Work through each section in order. Compute expected value with $E(X) = \sum x \cdot P(X = x)$: multiply each value by its probability, then add. Show each term as "value times its probability" before summing. For payoff problems, write losses as negative values. Remember that $E(X)$ is the mean of the distribution and need NOT be a value the variable can actually take.

Grade 11·22 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-md-a-2

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Fluency Practice

Compute each expected value as an explicit weighted sum. Write each term as value times its probability before adding.

In a game the net result $X$ is $+4$ dollars with probability $\tfrac{1}{4}$ and $-2$ dollars (a loss) with probability $\tfrac{3}{4}$ .

$x$ (dollars)	+4	-2
$P(X=x)$	1/4	3/4

Compute the expected net result $E(X)$ , in dollars. Keep the sign.