Main content

## Statistics and probability

### Course: Statistics and probability > Unit 9

Lesson 1: Discrete random variables- Random variables
- Discrete and continuous random variables
- Constructing a probability distribution for random variable
- Constructing probability distributions
- Probability models example: frozen yogurt
- Probability models
- Valid discrete probability distribution examples
- Probability with discrete random variable example
- Probability with discrete random variables
- Mean (expected value) of a discrete random variable
- Expected value
- Mean (expected value) of a discrete random variable
- Expected value (basic)
- Variance and standard deviation of a discrete random variable
- Standard deviation of a discrete random variable

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Expected value (basic)

Expected value uses probability to tell us what outcomes to expect in the long run.

## Problem 1: Board game spinner

A board game uses the spinner shown below to determine how many spaces a player will move forward on each turn. The probability is start fraction, 1, divided by, 2, end fraction that the player moves forward 1 space, and moving forward 2 or 3 spaces each have start fraction, 1, divided by, 4, end fraction probability.

## Problem 2: Basketball decisions

Kayla is a basketball player who makes 50, percent of her 2-point shots and 20, percent of her 3-point shots.

## Want to join the conversation?

- Wouldn't the expected value for a 2-point shot be 2 points? I understand what you're getting at, but this seems like asking what color Napoleon's white horse was.(21 votes)
- The idea ist that she will make half of her 2-point shots, scoring 2 points each, but also miss the other half, scoring 0 points each. So this, over time, will yield a result of approximately 1 point per shot.(89 votes)

- how do I find expected value(2 votes)
- expected value = value*probability(38 votes)

- If E(X)= µ, what is E(X− µ) ?(1 vote)
- The expected value of a difference is the difference of the expected values, and the expected value of a non-random constant is that constant. Note that E(X), i.e. the theoretical mean of X, is a non-random constant.

Therefore, if E(X) = µ, we have E(X − µ) = E(X) − E(µ) = µ − µ = 0.

Have a blessed, wonderful day!(11 votes)

- Hi just wondering what year/s is mathematics II ? and does anyone know any helpful sites i can do a exam of mathmatics 2 ?

#YouCanLearnAnything

thanks(3 votes)- It varies, you can find it in highschool courses but it covers a wide range of topics that are in a wide range of grades like it covers both probability, geometry, and trigonometry which varies across different grade levels and courses for those respective grade levels. Sorry for the 2 year late reply but...well...better late than never, right?(4 votes)

- How do you determine whether the odds are to your favor using the expected probability formula(2 votes)
- Give questions worth my time to answer and that make sense to answer at all. Never in my life will i need this.(0 votes)
- Expected values are used to decide on strategies in gambling games, determine whether or not a game is fair, test statistical hypotheses, and calculate insurance premiums.

It is best to assume that the math skills that you learn will be used at some time for something in your life.(11 votes)

- What is expected value?(1 vote)
- Expected value is the long-run average value of repetitions of the experiment it represents.

From: Wiki(3 votes)

- I need help with value. Can someone help?(1 vote)
- What do you need help with? I might be able to help if you narrow it down to the specific thing that you need help with(1 vote)

- If Expected Value is the 'Long-run' average, is there a way to calculate the 'Short-run'?(1 vote)
- The idea is that there is usually too much variability to get a "short-run" average. The only way to calculate a "short-run" average is to actually perform a set of events and see what the outcome was, but you need to be aware that the outcome might be drastically different if you performed the same series of events again. If you're flipping a coin, your first 10 flips could be all tails! Or no tails at all. The concept behind expected value is just that over many thousands of "flips", you are likely to get an equal number of heads and tails (if the probability of each outcome is 50%)(1 vote)

- oh i could've scrolled down here to get the answers the whole time, dang, missed opportunity(1 vote)