// File MIT-Lab-02-02-00-01.txt. Edition 12/29/2012. // Lab Specs // Title Card_Draw_Simulation // Problem Specs // PauseCheckbox(-1 checked 0 cleared) ` -1 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. ` -1 Experiment: Draw one card from a deck and then replace it. _ The list in the upper left hand corner of the window indicates the cards that are in the deck. By default, the 2 of Clubs, 3 of Hearts, 3 of Diamonds, and 4 of Hearts. Do not change the default settings. _ 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. ` -1 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? ` -1 3. Click the Continue 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 Continue button a few more times until you are convinced that the simulation is calculating the mean and variance of the numerical values correctly. ` 0 Now the Pause checkbox has been cleared. _ 4. Click the Continue 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?