Expected Value Practice B

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.

To calculate the expected value, multiply each possible outcome by its probability and sum all these products.

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

The mean is the average of a set of values, representing the central point of a probability distribution.

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

An outcome is a possible result of a random experiment or process.

The expected value is -$5.20, calculated as (1/1000 * 794) + (999/1000 * -6).

A negative expected value indicates a loss on average over time if the same bet or investment is repeated.

The expected number of children is 1.97, calculated as (0.3*1) + (0.43*2) + (0.27*3).

The expected value is $7.50, calculated based on the probabilities of each outcome.