# Segment 4. The Jailer's Tip

#### Watch this segment

(Don't worry, what you see out-of-focus below is not the beginning of the segment. Press the play button to start at the beginning and in-focus.)

{{#widget:Iframe |url=http://www.youtube.com/v/425D0CjLLLs&hd=1 |width=800 |height=625 |border=0 }}

The direct YouTube link is http://youtu.be/425D0CjLLLs

Links to the slides: PDF file or PowerPoint file

### Problems

#### To Calculate

1. Evaluate <math>\int_0^1 \delta(3x-2) dx</math>

2. Prove that <math>\delta(a x) = \frac{1}{a}\delta(x)</math>.

3. What is the numerical value of <math>P(A|S_BI)</math> if the prior for <math>p(x)</math> is a massed prior with half the mass at <math>x = 1/3</math> and half the mass at <math>x = 2/3</math>?

#### 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?