Homework 4

Due: Tuesday, November 13th (send your reports to my UU email address)

Sparse Stochastic Collocation

Description: In this assignment you will consider a simple stochastic function \(u(y_1,y_2) = y_1 + y_2\) where \(y_1, y_2 \sim U[1,6]\) are two uniformly and independently distributed random variables. Physically, \(u\) is like rolling two dice and taking the sum, except the dice are continuously distributed instead of discrete. The goal is to compute the first two statistical moments of \(u\).

Tasks:

1. Justify (in words) the use of stochastic spectral methods over Monte Carlo sampling approaches for computing the statistics of \(u\).
2. Compute (by hand) the expectation and the variance of \(u\) by sparse stochastic collocation, using the total degree rule with the following parameters: \(N=2\), \(L=1\), and \(p(i) = i\). Show your work.