AP Statistics
6-21 OBSERVING X - X
a) Let X be a random variable representing the number one if heads and two if tails when flipping a coin. Make a probability model for the distribution of X. (Make a table listing all possible outcomes and the associated probabilities.) Find the mean, variance, and standard deviation for X.
b) Physically, what would X - X represent? How would you record X - X using your one coin?
c) Record 20 observations of X - X. Make a dot plot for the 20 differences. Calculate the mean and standard deviation, and write a concise sentence describing the shape, center, and spread for the sample of differences.
d) Make a probability model for the distribution of X - X. (Make a table listing all possible outcomes and the associated probabilities.) Calculate the mean, variance, and standard deviation for X- X.
e) Compare your results from part (d) with your combined sample from part (c). How close were the observed sample statistics to the calculated values? What do you predict would happen if you had 400 observations of X - X rather than 40?
f) Write an explanation to a friend, not in this class, why X - X is not always zero. Discuss the expected value and standard deviation as part of your response.