Expected Value Practice

Front

What is the expected value in probability?

Back

The expected value is the average of all possible outcomes of a random variable, weighted by their probabilities.

Front

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

Back

Multiply each possible outcome by its probability and sum all these products.

Front

What is a discrete random variable?

Back

A discrete random variable is a variable that can only take on a countable number of distinct values.

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on any value within a certain range or interval.

Front

If a coin flip results in heads with a probability of 0.5 and tails with a probability of 0.5, what is the expected value if heads wins $4 and tails loses $3?

Back

$0.50

Front

In a lottery with 1000 tickets, if the prize is $800 and the ticket costs $6, what is the expected value of buying a ticket?

Back

-$5.20

Front

What is the formula for calculating expected value (EV)?

Back

EV = Σ (outcome × probability) for all outcomes.

Front

If 30% of households have 1 child, 43% have 2 children, and 27% have 3 children, what is the expected number of children in a randomly selected household?

Back

1.97

Front

What does it mean if a random variable is uniformly distributed?

Back

It means that all outcomes are equally likely.

Front

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

Back

A probability distribution shows the probabilities of all possible outcomes, while a CDF shows the probability that a random variable is less than or equal to a certain value.