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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.(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.(110 votes)

- how do I find expected value(1 vote)
- expected value = value*probability(39 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)
- In order to determine whether the odds are in your favor using the expected probability formula, you need to compare the expected value (or mean) with the potential outcomes. If the expected value is higher than the current situation or the alternative options, then the odds are generally in your favor. Conversely, if the expected value is lower, then the odds may not be as favorable.

For example, in Problem 2, Kayla's expected value for a 2-point shot is 1 point, while for a 3-point shot, it's 0.6 points. If Kayla consistently makes 2-point shots, she can expect to score an average of 1 point per shot. If she consistently makes 3-point shots, she can expect to score an average of 0.6 points per shot. Therefore, she should choose the option with the higher expected value to maximize her scoring potential.(1 vote)

- In problem 1, can someone reinterpret the problem please? Isn't that space 1 , 2 or 3 just the name of the certain area of the board game spinner? Why do we multiply the name by its probability ? I really don't understand the problem. Thanks in advance.(0 votes)
- Hi Tue Pham! When you spin the spinner, the result tells you how many spaces you get to move forward on an imaginary game board. Imagine a game where your goal is to get from "point A" to "point B", and to get there you move a certain number of spaces each turn. Sort of like this:
`START --- ( A ) --- ( B ) --- ( C ) --- ( D ) --- END`

If you spin and get a "3", you would move from START to A, B, and finally land on C (you would move 3 spaces forward). Does that help clarify?(3 votes)

- 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)
- The combined probability of Kayla making a 2-point shot and a 3-point shot is not necessarily equal to 1 because she might miss both types of shots. In this scenario, if Kayla misses both types of shots, the combined probability would be less than 1.

It's important to understand that the probabilities provided represent the likelihood of specific outcomes (i.e., making a 2-point shot or making a 3-point shot) and do not necessarily guarantee that one of the outcomes will occur. The sum of these probabilities indicates the total probability space for all possible outcomes, but it doesn't have to equal 1 in this case because there are other potential outcomes not explicitly mentioned (such as missing both types of shots).(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)