Expected Value Practice

Front

What is the expected value in probability and statistics?

Back

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.

Front

How do you calculate the expected value of a discrete random variable?

Back

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

Front

What is the formula for expected value (E) of a discrete random variable X?

Back

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

Front

If a game has an expected value of $0, what does that imply for the player?

Back

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

Front

What does a negative expected value indicate about a game?

Back

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

Front

In the context of expected value, what does 'fair game' mean?

Back

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

Front

How do you find the expected value of a spinner with different outcomes?

Back

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

Front

What is the expected value of rolling a fair die?

Back

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

Front

In the example of a spinner, if red wins $23 with a probability of 0.4, yellow wins $175 with a probability of 0.15, and green loses $50 with a probability of 0.45, how do you calculate the expected value?

Back

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

Front

What is the expected value of a random variable that can take on values 1, 2, and 3 with probabilities 0.2, 0.5, and 0.3 respectively?

Back

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