A Markov chainX0, X1, X2. . .on states 0,1,2 has the transition probability

matrix

0.1 0.3 0.6

P=0.8 0.1 0.10.2 0.3 0.5

andinitialdistributionp0=P(X0=0)=0.7,p1=P(X0=1)=0.1,p2=P(X0=2)=0.2. Determine

a)P(X0=0,X1=2,X2=1).

b)P(X0=1,X1=1,X2=2).

c)P(X2=0,X3=2|X1=0).

d)P(X1=2,X2=1|X0=1).

e)P(X1=1,X2=2,X3=0).

f) Calculate the two-step transition matrixP2. g)WhatisP(X3=2|X1=0)?