Compute the area under the function given by integration

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Reference no: EM131396266

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

Reference no: EM131396266

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