<p>Random Variable: A variable that is currently undefined with an attached probability.</p><p><br></p><p>Defining them is important to quantify outcomes.</p>

1. Random Variables

<p>Discrete: distinct, individual value</p><p>Continous: any value in an interval</p><p><br></p><p>The difference between them is akin to integers vs any number.</p>

2. Discrete and Continous RV

<p>0 = 0% chance of occurring</p><p>1 = 100% chance of occurring</p><p>Knowing that something will happen, all probabilities add up to 1.  Mapping out the outcomes and quantifying them allows us to calculate the individual probabilities.</p>

3. Constructing a Distrubution for D RV

<p>1. First always find relative frequencies.</p><p>2. All models must add up to 1 or 100%</p><p>3.  These models can then be put in graphs or charts or otherwise presented</p>

4. Probability Models

<p>1. Calculate mean by taking the possible value of the variable and multiplying it by the probability of said value</p><p>2. Then add all values together and divide by total number of values, like a normal average.</p><p>The result is not exact for every situation, but acts as a good assumption.</p>

5. Mean/expected Value Of D RV

<p>Variance = sum of all possible values minus the mean, squared, times the relative probability.</p><p>Ie: (0-3.4)^2 x 0.32 + (1-3.4)^2 x 0.32....</p><p>Standard deviation = square root of variance</p><p>- denoted with sigma</p><p>- represents on average how far off actual values are from the calculated mean.</p>

6. Variance And Standard Deviation Of D RV

<h4><a href="https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/test/random-variables-stats-library-unit-test?modal=1">Unit test</a></h4><div><span>Level up on all the skills in this unit and collect up to 2100 Mastery points!</span></div><div><button type="button" data-test-id="test-open-modal-button" role="button" tabindex="0"><span>Start Unit test</span></button></div><h3>About this unit</h3><div><span>Random variables can be any outcomes from some chance process, like how many heads will occur in a series of 20 flips. We calculate probabilities of random variables and calculate expected value for different types of random variables.</span></div><p>Our mission is to provide a free, world-class education to anyone, anywhere.</p><p dir="ltr">Khan Academy is a 501(c)(3) nonprofit organization. <a href="https://www.khanacademy.org/donate" dir="ltr">Donate</a> or <a href="https://www.khanacademy.org/contribute" dir="ltr">volunteer</a> today!</p>

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Random variables | Statistics and probability | Math