Back to Calculate the expected value of a random variable — Problem 1 · 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

Warm-Up: Distributions and Weighted Means

These problems review probability distributions and the weighted-average idea you already know.

A random variable $X$ has the probability distribution below.

$x$	0	1	2
$P(X=x)$	1/4	1/2	1/4

Which expression correctly sets up the expected value $E(X)$ ?

$0 \cdot \tfrac{1}{4} + 1 \cdot \tfrac{1}{2} + 2 \cdot \tfrac{1}{4}$

$\dfrac{0 + 1 + 2}{3}$

$\dfrac{1}{4} + \dfrac{1}{2} + \dfrac{1}{4}$

$0 + 1 + 2$