For this homework, you are expected to develop several simulation algorithms for a squareroot diffusion {Xt:t0} which satisfies the SDE, dXt=(bXt)dt+XtdWt,t0, with X0=x0. 1. Propose a method to simulate the Poisson random variable NPoisson(). P[N=k]=ek!k,k=0,1,2, 2. A chi-square random variable Y with degree of freedom (d.o.f.) >0 has density function fY(x)=2/2(/2)1x/21ex/2,x>0. (a) Propose an acceptance-rejection (AR) method to simulate Y exactly. (Hint: you can consider the cases 2 and 0