Expected Value Statistics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
A spinner has outcomes: \1 (prob 0.5), \3 (prob 0.3), \$10 (prob 0.2). Find the expected value.

Solution

  1. 1
    Step 1: E(X)=1(0.5)+3(0.3)+10(0.2)E(X) = 1(0.5) + 3(0.3) + 10(0.2).
  2. 2
    Step 2: E(X)=0.5+0.9+2.0=$3.40E(X) = 0.5 + 0.9 + 2.0 = \$3.40.

Answer

E(X)=$3.40E(X) = \$3.40
Expected value is the weighted average of all outcomes, where the weights are probabilities. It predicts the average payoff over many spins.

About Expected Value

The expected value of a random variable is the long-run average outcome of a random process, calculated as the weighted sum of each possible outcome times its probability. It represents what you would earn or lose on average per trial if the process were repeated infinitely many times.

Learn more about Expected Value โ†’

More Expected Value Examples

Example 1 medium

A game costs [formula]10; otherwise, you win nothing. Find the expected value per game.

Example 2 medium

A raffle sells 200 tickets at [formula]500. Find the expected value for a ticket buyer.

Example 4 medium

A game costs [formula]20 with probability 0.1, [formula]0 otherwise. Find the expected net value of

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