Problem 1
Assume that breast cancer affects .8 percent of the female population between 40 and 50 years of age. There are two kinds of test results: true positive (you have it) and false positive (the test indicates you do have it, but you really do not). Assume Mammograms are 90% accurate at spotting people who have breast cancer (true positive), and are 93% accurate at spotting people who do not (true negative). What are the false negative and false positive accuracies? If a female tests positive for breast cancer, compute the likelihood that she indeed has the cancer.
Problem 2
A pair of dice is rolled. The sum of the faces on top is observed. What are the expectation, variance, and standard deviation of the observed sum? The Expectation and Variance Template attached to the main posting is optional and recommended.