//  File MIT-Lab-02-02-00-01.txt. Edition 2/26/2020.


//  Lab Specs
//     Title
         Card_Draw_-_Mean_and_Variance

//  Problem Specs
//    PauseCheckbox(-1 checked 0 cleared)


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Objective: Illustrate the relative frequency interpretation of probability
 by focusing on the distribution's mean (center) and variance (spread).
 That is, show that after many, many repetitions of the experiment,
 the mean and variance of the random variable's numerical values
 mirrors the mean and variance of the random variable's probability
 distribution.
_
Scroll down the list of cards and select four to be in the deck: 2 of Clubs,
 3 of Hearts, 3 of Diamonds, and 4 of Hearts.
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Experiment: Draw one card from a deck and then replace it.
_
The list in the upper left corner of the window indicates the cards that are
 in the deck. Be certain that the 2 of Clubs, 3 of Hearts, 3 of Diamonds,
 and 4 of Hearts are selected.Next
_
Let v equal the "value" of the card drawn; that is, v equals 2 if the 2 of Clubs is drawn,
 3 if the 3 of Hearts or the 3 of Diamonds is drawn, and 4 if the 4 of Hearts is drawn.

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1. Using the appropriate equations, calculate the mean and variance of the the
 random variable v's probability distribution?
_
2. Click the Start button. Which card was drawn from the deck? What does numerical value
 of v equal on the first repetition of the experiment?

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3. Click the Next button to repeat the experiment for a second time. 
 What does numerical value of v equal on the second repetition of the experiment?
 Calculate the mean and variance of the numerical values for the first two repetitions.
 Compare the simulation's calculations of the mean and variance with your calculations.
 Click the Next button a few more times until you are convinced that the simulation
 is calculating the mean and variance of the numerical values correctly.

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Now the Pause checkbox has been cleared.
_
4. Click the Next button. 
 After many, many repetitions click the Stop button. What are mean and variance
 of the numerical values v's after many, many repetitions?
_
5. Compare your answers to 1 and 4. How is the mean of the probability
 distribution related to the mean of the numerical values after many, many
 repetitions? How is the variance of the probability distribution related
 to the variance of the numerical values after many, many repetitions?