Answer the following interview-style probability/statistics questions. Provide formulas and short explanations. 1) **Bayes’ rule:** State Bayes’ rule. Given a disease prevalence \(P(D)=1\%\), a test sensitivity \(P(+\mid D)=0.99\), and false positive rate \(P(+\mid \neg D)=0.05\), compute \(P(D\mid +)\). 2) **Controls in regression:** In an observational setting, why might adding control variables change the estimated coefficient on a variable of interest? When can adding controls introduce bias? 3) **CLT:** State the Central Limit Theorem and its practical implication for the sampling distribution of the sample mean. 4) **Uniform distribution moments:** If \(X\sim \mathrm{Unif}(a,b)\), compute \(E[X]\) and \(\mathrm{Var}(X)\). 5) **Hypothesis test / t-stat:** For testing \(H_0: \mu=\mu_0\) with sample mean \(\bar x\), sample standard deviation \(s\), and sample size \(n\), write the one-sample t-statistic. 6) **Effect size vs MDE:** Define effect size and Minimum Detectable Effect (MDE). How do power, variance, sample size, and alpha affect MDE?