Expected Value

Front

What is the expected value in probability and statistics?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by their respective probabilities.

Front

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

Back

To calculate the expected value, multiply each possible outcome by its probability and then sum all these products.

Front

In the context of expected value, what does it mean if the expected value is greater than zero?

Back

If the expected value is greater than zero, it indicates a potential profit or gain in the long run.

Front

What does it indicate if the expected value is less than zero?

Back

If the expected value is less than zero, it indicates a potential loss in the long run.

Front

What is the expected value of rolling a fair six-sided die?

Back

The expected value of rolling a fair six-sided die is 3.5.

Front

If you win $12 for rolling a six and $6 for rolling a one on a die, how do you find the expected value of this game?

Back

Calculate the expected value by multiplying the winnings by their probabilities: (1/6 * $12) + (1/6 * $6) + (4/6 * $0) = $3.

Front

What is the expected value of a game where you pay $1 to roll a die and win $3 if you roll a 2 or a 4?

Back

The expected value is calculated as: (1/3 * $3) + (2/3 * $0) - $1 = $0.

Front

What is the significance of the expected value in decision-making?

Back

The expected value helps in making informed decisions by providing a measure of the average outcome of uncertain events.

Front

How does the concept of expected value apply to gambling?

Back

In gambling, the expected value helps players understand the average outcome of their bets over time, guiding their strategies.

Front

What is a common misconception about expected value?

Back

A common misconception is that the expected value guarantees a specific outcome in a single trial; it only represents the average over many trials.