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Objective:
To understand how to sample from different distributions, and to understand the link between samples and a PDF/PMF. To explore different parameter settings of common distributions, and to implement a small library of random variable types.
Deliverable:
You should turn in an ipython notebook that implements and tests a library of random variable types.
When run, this notebook should sample multiple times from each type of random variable; these samples should be aggregated and visualized, and compared to the corresponding PDF/PMF. The result should look something like this:
Description:
You must implement:
* The following one dimensional, continuous valued distributions. For these, you should also plot the PDF of the random variable on the same plot; the curves should match.
Beta (alpha=1, beta=3)Poisson (lambda=7)Univariate Gaussian (mean=2, variance=3)
* The following discrete distributions. For these, plot predicted and empirical histograms side-by-side:
Bernoulli (p=0.7)Multinomial (theta=[0.1, 0.2, 0.7])
* The following multidimensional distributions.
- Two-dimensional Gaussian
- 3-dimensional Dirichlet
Hints:
The following functions may be useful to you:
hist( data, bins=50, normed=True ) numpy.linspace legend title
