Prob 2.2 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

Multiply each possible value of the random variable by its probability and sum all these products.

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

1.97

Front

If a probability distribution has values 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively, what is the expected value?

Back

14

Front

What does it mean if the expected value is negative?

Back

It indicates that, on average, you are expected to lose or not gain.

Front

What is the average number of customers expected to make a purchase if the expected value is 3.0?

Back

3.0 customers.

Front

What is a probability distribution?

Back

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

Front

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

Back

The probabilities must sum to 1, representing the certainty that one of the outcomes will occur.

Front

What is the formula for expected value (E(X))?

Back

E(X) = Σ [x * P(x)], where x is a value and P(x) is the probability of x.

Front

What is the expected value of a random variable with outcomes 0, 1, 2, and their probabilities 0.2, 0.5, 0.3 respectively?

Back

E(X) = (0*0.2) + (1*0.5) + (2*0.3) = 1.1.