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{:[P={:[0,0,1],[1,0.4,0.6],[0.2,0.8]:}],[P(x_(0)=0)=1//3],[P(x_(0)=1)=2//3]:}a) P(x_(4)=0∣x_(2)=1)we have to calculate p_(10)^((2))for that we find {:p^(2))=P**p{:[{:[[[0.4,0.6],[0.2,0.8]][[0.4,0.6],[0.2,0.8]]=[[0.16+0.12,0.24+0.48],[0.08+0.16,0.12+0.64]]],[=[[0.28,0.72],[0.24,0.76]]],[P_(10)^((2))=0.24[(i,1.0 ... See the full answer