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Chapter 12 practice bank

100 questions:
Advanced Bayes

Solve on paper first. Reveal only the final answer when you want to check yourself. There are no worked solutions in this bank by design.

34 easy 33 medium 33 advanced

EasyMarginalizationadvanced-probability-bayesian-reasoning-1

A joint PMF has p(X=1,Y=0)=2/20 and p(X=1,Y=1)=3/20. Find P(X=1).

EasyTower propertyadvanced-probability-bayesian-reasoning-2

P(Y=1)=3/10, E[X|Y=0]=1, and E[X|Y=1]=5. Find E[X].

EasyBayesian model comparisonadvanced-probability-bayesian-reasoning-3

P(H₁)=0.3, P(E|H₁)=0.6, and P(E|H₂)=0.2. Find P(H₁|E).

EasyBeta-binomial updateadvanced-probability-bayesian-reasoning-4

With prior Beta(2,3), observe 4 successes and 2 failures. Give the posterior.

EasyPosterior expected lossadvanced-probability-bayesian-reasoning-5

P(sick)=0.1. Treating a healthy person costs 1; missing sickness costs 10. Which action has smaller expected loss?

EasyMarkov inequalityadvanced-probability-bayesian-reasoning-6

Nonnegative X has E[X]=3. Give Markov's upper bound on P(X≥12).

EasyChebyshev inequalityadvanced-probability-bayesian-reasoning-7

Give Chebyshev's upper bound for being at least 2 standard deviations from a finite-variance mean.

EasyPosterior predictiveadvanced-probability-bayesian-reasoning-8

A posterior gives weight 0.2 to Bernoulli p=0.3 and the rest to p=0.8. Find the predictive success probability.

EasyMarginalizationadvanced-probability-bayesian-reasoning-9

A joint PMF has p(X=1,Y=0)=3/20 and p(X=1,Y=1)=4/20. Find P(X=1).

EasyTower propertyadvanced-probability-bayesian-reasoning-10

P(Y=1)=4/10, E[X|Y=0]=2, and E[X|Y=1]=6. Find E[X].