Discuss the below in detail:
Given: 8 cases of invasive cancer and a total years of employment of 145 teachers. The cancer institute statistcis suggest 4.2 cases of cancer could be expected to occur.
Assumptions: 145 employees develop or do not develop cancer independently and chances of cancer for each employee is the same. Therefore N, the number of cancers among the 145 employees, has a binomial distribution.
P(n/O) = (145/n) o^n (1-O) ^145-n in which (145/n) is the combination of 145 things taken n at a time. Assume uniform distribution (1,0)
f(O) =1 for theta (O) between 0 and 1
Use Bayes rule to update the prior distribution to a posterior distribution f(O/n=8) based on 8 observed cases O=theta Theta is the Chance of Cancer.