PLEASE ANSWER PARTS A, C, AND D. Thank you!
2.2 For diagnostic testing, let X = true status (1 = disease, 2= no disease) and Y = diagnosis (1 = positive, 2 = negative). Let?i = P (Y = 1|X = i), i = 1, 2.
a. Explain why sensitivity = ?1 and specificity = 1 ? ?2.
c. For mammograms for detecting breast cancer, suppose ? = 0.01,sensitivity = 0.86, and specificity = 0.88. Given a positive testresult, find the probability that the woman truly has breastcancer.
d. To better understand the answer in (c), find the jointprobabilities for the 2 × 2 cross-classification of X and Y .Discuss their relative sizes in the two cells that refer to apositive test result.
