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Develop an appropriate routine for sampling.

1. Find the inverse distribution function (F −1) for y|x in the bivariate planar density; that is, show how a U(0, 1) sample must be transformed to be a draw from y|x.

2. Develop a rejection sampler for sampling data from the bivariate planar density f(x) ∝ 2x + 3y + 2.

3. Develop an inversion sampler for sampling data from the linear density f(x) ∝ 5x + 2. (Hint: First, find the normalizing constant, and then find the inverse function).

4. Develop an appropriate routine for sampling the λ parameter from the Poisson distribution voting example in the previous chapter.

Solution:

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