Problem Set 6 | Assignments | Introduction to Probability and Statistics | Mathematics

Problem Set 6 Answer Checker

Work on the assigned problems in the associated Problem Set PDF file, then use the problem set checker to find out if the answer was correct or incorrect. To check your answers put them in the appropriate box and click the 'Check' button. Every checker box can do arithmetic and calculate standard functions (see calculator help). If you give decimal answers, give them to at least 3 decimal places.

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Problem 1.

(a) Give the Bayes' factor for

H_0

vs.

H_1

(b) No online check

(d) For each of the priors give the value of the posterior pdf at $θ = 0.6$

Prior (d.i):

Prior (d.ii):

Prior (d.iii):

Prior (d.iv):

Prior (d.v):

(e) Give the posterior probability of heads for each prior.

Prior (e.i):

Prior (e.ii):

Prior (e.iii):

Prior (e.iv):

Prior (e.v):

(f) Give the posterior odds of $H_1$ vs. $H_0$ for each prior.

Prior (f.i):

Prior (f.iv):

Problem 2.

Give the posterior odds that Alice filled in for Bob.

Problem 3.

(a.i) Evaluate the posterior pdf for the data

x= 0.2

θ = 0.3

(a.ii) Evaluate the posterior pdf for the data $x = 0.2$ at $θ = 0.1$ .

(b.i) Evaluate the posterior pdf for the data $(0.1,0.5)$ at $θ = 0.7$ .

(b.ii) Evaluate the posterior pdf for the data $(0.5, 0.5)$ at $θ = 0.7$ .

(b.iii) Evaluate the posterior pdf for the data $(0.1, 0.2, 0.3, 0.4, 0.5)$ at $θ = 0.7$ .

(d) Give the MAP when $x = 0.6

(e) No online check

Problem 4.

(a) No online check

(b) No online check

(d.i) Give the expected value (mean) for Randall's posterior pdf.

(d.ii) Give the expected value (mean) for Mary's posterior pdf.

Problem 5.

(5.i) Give the prior odds the chosen die is 4-sided.

(5.ii) Give the posterior odds that the chosen die is 4-sided after roll 1.

(5.iii) Give the posterior odds that the chosen die is 4-sided after roll 2.

(5.iv) Give the posterior odds that the chosen die is 4-sided after roll 3.

(5.v) Give the posterior odds that the chosen die is 4-sided after roll 4.

(5.vi) Give the posterior odds that the chosen die is 4-sided after roll 5.