Expected Value Practice

The expected value is a measure of the center of a probability distribution, representing the average outcome of a random variable if the experiment were repeated many times.

Multiply each possible outcome by its probability and sum all these products.

E(X) = Σ [x * P(x)], where x is a possible outcome and P(x) is the probability of that outcome.

The player can expect to neither win nor lose money in the long run.

It indicates that the player is expected to lose money over time.

A fair game is one where the expected value is zero, meaning players neither gain nor lose money on average.

Calculate the expected value by multiplying the value of each outcome by its probability and summing these products.

The expected value is 3.5, calculated as (1+2+3+4+5+6)/6.

E = (0.4 * 23) + (0.15 * 175) + (0.45 * -50) = $12.95.

E(X) = (1 * 0.2) + (2 * 0.5) + (3 * 0.3) = 2.1.