Expected Value Practice

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. The sum of all probabilities must equal 1.

Front

What are the conditions for a valid probability distribution?

Back

1. All probabilities p(x) must be between 0 and 1. 2. The sum of all probabilities must equal 1.

Front

What is a discrete random variable?

Back

A discrete random variable is a variable that can take on a countable number of distinct values.

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on an infinite number of values within a given range.

Front

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

Back

The expected value (E) is calculated by summing the products of each possible value and its corresponding probability: E(X) = Σ [x * p(x)].

Front

What is the expected value of a game where you pay $2 to play, and the outcomes are: lose (red), win $2 (green), win $5 (blue)?

Back

The expected value is -$0.50.

Front

What does it mean if the expected value is negative?

Back

A negative expected value indicates that, on average, you will lose money if you play the game repeatedly.

Front

What is the average number of customers expected to make a purchase if the probability distribution indicates an average of 3.0?

Back

The average number of customers expected to make a purchase is 3.0.

Front

What is the significance of the sum of probabilities in a probability distribution?

Back

The sum of probabilities must equal 1, ensuring that all possible outcomes are accounted for.

Front

What is an example of a discrete random variable?

Back

The number of goals scored in a soccer match is a discrete random variable.