Segment 8. Some Standard Distributions

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Watch this segment

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

The direct YouTube link is http://youtu.be/EDYDC7iNGTg Links to the slides: PDF file or PowerPoint file

Problems

To Calculate

1. In Segment 6 (slide 8) we used the improper prior Failed to parse (unknown error): 1/r . Show that this is just a limiting case of a (completely proper) Lognormal prior.

2. Prove that Failed to parse (unknown error): {\rm Gamma}(\alpha,\beta) has a single mode at Failed to parse (unknown error): (\alpha-1)/\beta when Failed to parse (unknown error): \alpha \ge 1 .

3. Show that the limiting case of the Student distribution as Failed to parse (unknown error): \nu\rightarrow\infty is the Normal distribution.

To Think About

1. Suppose you have an algorithm that can compute a CDF, Failed to parse (unknown error): P(x) . How would you design an algorithm to compute its inverse (see slide 9) Failed to parse (unknown error): x(P) ?

2. The lifetime t of a radioactive nucleus (say Uranium 238) is distributed as the Exponential distribution. Do you know why? (Hint: What is the distribution of an ExponentialFailed to parse (unknown error): (\beta) random variable conditioned on its being greater than some given value?)

Class Activity

problem statement: ClassActivity20130204.pdf

data file for class activity: events20130204.txt

Jeff's solution (Python)

Bill's solution (MATLAB)