Back to Calculate the expected value of a random variable — Problem 4 · 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

Work through problems with immediate feedback

Fluency Practice

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

A carnival game pays out an amount $X$ per play according to the distribution below.

$x$ (dollars)	0	2	5
$P(X=x)$	0.6	0.3	0.1

If a player plays this game many, many times, what is the long-run average payout per play (in dollars)? Compute $E(X)$ .