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Bayes Theorem for invasive cancer research

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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. I don't have the theta symbol on my computer.

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This solution helps with a question that uses the Bayesian Theorem based on the assumption the 145 employees do or do not develop cancer independently. Step by step calculations are given along with explanations.

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Bayes Theorem
Given: 8 cases of invasive cancer and a total years of employement of 145 teachers. The cancer institute statistis suggest 4.2 cases of cancer could be expected to occure.

Assumptions 145 employees develop or not develop cancer independently and chances of cancer for each employee is the same. Therefore N the # of cancers among the 145 employees has a binomial distribution.

P(n/O) = (145/n) o^n (1-O) ^145-n in which ...

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