Segment 4. The Jailer's Tip
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2. Prove that .
3. What is the numerical value of if the prior for is a massed prior with half the mass at and half the mass at ?
To Think About
1. With respect to problem 3, above, since x is a probability, how can choosing x=1/3 half the time, and x=2/3 the other half of the time be different from choosing x=1/2 all the time?
2. Suppose A is some event that we view as stochastic with P(A), such as "will it rain today?". But the laws of physics (or meteorology) say that A actually depends on other weather variables X, Y, Z, etc., with conditional probabilities P(A|XYZ...). If we repeatedly sample just A, to naively measure P(A), are we correctly marginalizing over the other variables?
Surprise Quiz (with Bill's solutions here) (Notice in the figure the almost perfect correlation between the peer ranks that the teams assigned and the TA's separate grading.)
We also discussed Mr. and Mrs. Smith and their daughter(s) -- see Think About Question 3 in Segment 3.
We also did some variants of Expected values and continuous distributions