Expected Value Practice

Front

What is the expected value in probability?

Back

The expected value is a measure of the center of a probability distribution, 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

To calculate the expected value (E(X)), use the formula: E(X) = Σ [x * P(x)], where x is a value and P(x) is its probability.

Front

What does it mean if the expected value is greater than the average of the outcomes?

Back

It indicates that the outcomes are skewed towards higher values, suggesting a higher likelihood of obtaining larger results.

Front

What is a probability distribution?

Back

A probability distribution describes how the probabilities are distributed over the values of a random variable.

Front

What is the difference between a probability distribution and a cumulative distribution function (CDF)?

Back

A probability distribution gives the probability of each outcome, while a CDF gives the probability that a random variable is less than or equal to a certain value.

Front

What is a valid probability distribution?

Back

A valid probability distribution must satisfy two conditions: all probabilities must be between 0 and 1, and the sum of all probabilities must equal 1.

Front

If a random variable has outcomes 1, 2, and 3 with probabilities 0.2, 0.5, and 0.3 respectively, what is the expected value?

Back

E(X) = (1*0.2) + (2*0.5) + (3*0.3) = 0.2 + 1.0 + 0.9 = 2.1.

Front

What is the expected number of cars in a randomly chosen American household if the probabilities are 0.5 for 1 car, 0.3 for 2 cars, and 0.2 for 3 cars?

Back

E(X) = (1*0.5) + (2*0.3) + (3*0.2) = 0.5 + 0.6 + 0.6 = 1.7.

Front

What is the expected value of a random variable that takes the values 10, 20, and 30 with probabilities 0.1, 0.3, and 0.6 respectively?

Back

E(X) = (10*0.1) + (20*0.3) + (30*0.6) = 1 + 6 + 18 = 25.

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.