Expected Value Practice

Front

What is the expected value of a random variable?

Back

The expected value (EV) is a measure of the center of a probability distribution, calculated as the sum of all possible values of the random variable, each multiplied by its probability.

Front

How do you calculate the expected value from a probability distribution table?

Back

Multiply each value of the random variable by its corresponding probability and sum the results.

Front

Given the probability model: X = {50, 20, 5} and P(X) = {0.1, 0.3, 0.6}, what is the expected value?

Back

EV = (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 14.

Front

What is the expected number of children in a household if 30% have 1 child, 43% have 2 children, and 27% have 3 children?

Back

EV = (1 * 0.3) + (2 * 0.43) + (3 * 0.27) = 1.97.

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 conditions for a valid probability distribution?

Back

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

Front

Is the following a valid probability distribution? P(X) = {0.2, 0.5, 0.3}

Back

Yes, because all probabilities are between 0 and 1 and their sum equals 1.

Front

Is the following a valid probability distribution? P(X) = {0.1, 0.4, 0.6}

Back

No, because the sum of probabilities (0.1 + 0.4 + 0.6 = 1.1) exceeds 1.

Front

What is the expected number of cars for a randomly chosen American household if the expected value is 1.75?

Back

The expected number of cars is 1.75.

Front

In a game where rolling a red die loses, green pays $2, and blue pays $5, how do you calculate the expected value?

Back

EV = (0 * P(red)) + (2 * P(green)) + (5 * P(blue)) - cost to play.