# Difference between revisions of "Eleisha's Segment 8: Some Standard Distributions"

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<b> To Think About </b> | <b> To Think About </b> | ||

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1. Suppose you have an algorithm that can compute a CDF, P(x). How would you design an algorithm to compute its inverse (see slide 9) x(P)? | 1. Suppose you have an algorithm that can compute a CDF, P(x). How would you design an algorithm to compute its inverse (see slide 9) 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 Exponential(\beta) random variable conditioned on its being greater than some given value?) | 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 Exponential(\beta) random variable conditioned on its being greater than some given value?) |

## Revision as of 13:04, 5 February 2014

** To Calculate **

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

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

3. Show that the limiting case of the Student distribution as \nu\rightarrow\infty is the Normal distribution.

** To Think About **

1. Suppose you have an algorithm that can compute a CDF, P(x). How would you design an algorithm to compute its inverse (see slide 9) 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 Exponential(\beta) random variable conditioned on its being greater than some given value?)