Segment 4. The Jailer's Tip

From Computational Statistics (CSE383M and CS395T)
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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?

Class Activities

Expected values and continuous distributions

Parsing text files