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## 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

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# 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 $\frac{1}{2}$ that the player moves forward $1$ space, and moving forward $2$ or $3$ spaces each have $\frac{1}{4}$ probability.

## Problem 2: Basketball decisions

Kayla is a basketball player who makes $50\mathrm{\%}$ of her $2$ -point shots and $20\mathrm{\%}$ 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.(22 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.(103 votes)

- how do I find expected value(1 vote)
- expected value = value*probability(37 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!(12 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?(6 votes)

- How do you determine whether the odds are to your favor using the expected probability formula(1 vote)
- 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.(13 votes)

- oh i could've scrolled down here to get the answers the whole time, dang, missed opportunity(1 vote)
- I finished it and it does not tell me that I have it done what do I do(1 vote)
- For question 1, is the spinner fair ?(1 vote)
- why the combined probability of 2 and 3-points are not 1?(1 vote)