Программный код на Python

1. Draw the plots for pdf's for Gaussian, Student, Laplacian distributions with the similar parameters. Compare the results.

2. Using statistical simulations methods (Monte-Carlo) check the correctness of central limit theorem.

3. Deriving the inverse gamma density. 

Let X ~ Ga(a,b) and Y = 1 / X. Show analytically, that Y ~ IG(a,b), i.e.,

IG(x|shape = a,scale = b) = b^a / Γ(a) x^{−(a+1)} e^{−b/x}.

Check the derived result using statistical simulation method (compare pds plot with hystogram).