Expected Value Spiral Review

Front

What is the expected value in probability?

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 its probability.

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 a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

What are the characteristics of a valid probability distribution?

Back

1. The sum of all probabilities must equal 1. 2. Each probability must be between 0 and 1.

Front

What does it mean if the expected value is negative?

Back

A negative expected value indicates that, on average, a player can expect to lose money in the long run.

Front

What is the mean of a probability distribution?

Back

The mean is another term for the expected value, representing the average outcome.

Front

How do you find the mean of a probability distribution from a table?

Back

Multiply each outcome by its probability, then sum all the products.

Front

What is the standard deviation in probability?

Back

The standard deviation measures the amount of variation or dispersion in a set of values.

Front

How is standard deviation calculated for a probability distribution?

Back

1. Find the expected value (mean). 2. For each outcome, subtract the mean and square the result. 3. Multiply by the probability of each outcome. 4. Sum these values and take the square root.

Front

What is a fair game in probability?

Back

A fair game is one where the expected value is zero, meaning neither the player nor the house has an advantage.