Assignment: Monte Carlo Integration
Pattern Recognition
1. A direct application for random number generation is in evaluating an integral. This approach is known as Monte Carlo Integration.
a) Evaluate the following integrals by the Monte Carlo method
I1= ∫_0^1e^(-x) dx?
I2= ∫_0^3(1-x^2 )^2 dx
Compute the area under the function given above by integration
Compare the areas obtained by method a) and b). If there is a discrepancy, explain the results.
2. Evaluate the following integral by Monte Carlo Integration
∞∫∞ e{-½((x - μ) / σ)^2} dx
For µ=0, σ = 1
For µ=10, σ = 4