Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density function f(y) = 1 4 ey/4, y 0, 0, elsewhere. (a) Critics would certainly consider the product a bargain if it is unlikely to require a major repair before the sixth year. Comment on this by determining P(Y > 6). (b) What is the probability that a major repair occurs in the first year?

Conditional Probability: probability of an event, given that another event has occurred P(A| B) is the probability of A, given that B has occurred P(A| B) is not the same as P(B|A) If events are independent then P(A)=P(A|B) and P(B)=P(B|A) A contingency table (two way table) is a visual representation of the relationships between the variable. They make probabilities easier to figure out. Levels of the explanatory variables are the rows of the table and response variables are the columns Risk=Number in category/Total number in group We can use a contingency table to calculate Relative Risk= risk in category 1/ risk in category 2 Baseline risk Percent change in risk= (relative risk – 1) 100% Positive means risk increases Negative means risk decreases If relative risk is 1 then the