Expected Value Practice B

Front

What is the expected value in probability?

Back

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.

Front

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

Back

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

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

Define 'mean' in the context of probability distributions.

Back

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

Front

What is the formula for expected value (E) of a discrete random variable X?

Back

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

Front

In the context of expected value, what does 'outcome' refer to?

Back

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

Front

What is the expected value of a lottery ticket that costs $6 with a prize of $800 and 1000 tickets sold?

Back

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

Front

How do you interpret a negative expected value?

Back

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

Front

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

Back

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

Front

What is the expected value of a game where you win $5 for 1 tail, $15 for 2 tails, and $40 for 3 tails when flipping a coin 3 times?

Back

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