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### 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.(23 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.(104 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)
- 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)
- What is expected value?(0 votes)
- Expected value is the long-run average value of repetitions of the experiment it represents.

From: Wiki(2 votes)