0 . Conditional probability: P(AB) = PAB) PIB) PAB) P(В). • Bayes' Ruleſ P(BA) P[ABP(E)=P(ABP(B) • Binomial Distribution

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0 . Conditional probability: P(AB) = PAB) PIB) PAB) P(В). • Bayes' Ruleſ P(BA) P[ABP(E)=P(ABP(B) • Binomial Distribution: P(X = x) = ()p*q*-* • Cumulative Distribution: F(x) = P(X < x) = f(x) • Expected value: E(X) = Ş«f() 1. (a) You wake up one day with red spots on your face. You call a doctor, who tells you that 90% of people who have smallpox have your symptoms, and the chance of a healthy person developing your symptoms is 8,1%. Since smallpox is fatal, you are naturally terrified. However, after you think for a while, you realise that the information the doctor gave you isn't really what you want to know. You do some research on line and learn that the prevalence of smallpox in the general population is one in a thousand. What is it that you want to know, and what is the answer?