Expectations of Functions:
Let X be distributed over the set N of non-negative integers, with probability mass function:
for above to be valid:
1)P(x) =1
here P(x) =*(1/20+1/21+1/22+1/23+...) =*(1/(1-1/2)) =1
=1/2
2) E(X)=xP(x) =(1/2)*(0*1/20+1/21+2/22+3/23+...) =(1/2)*(1/2)/(1-1/2)2 =1
3)P(Y=1) =P(X=1)+P(X=4)+P(X=7)+P(X=8)+..... =(1/2)2+(1/2)5+(1/2)8+.... =(1/4)/(1-1/8)=2/7
4)
E(Y)=0*(P(X=0)+P(X=3)+P(X=6)+...)+1*(P(X=1)+P(X=4)+P(X=7)+..)+2*(P(X=2)+P(X=5)+P(X=8)+..)
=1*(2/7)+2*(1/7)=4/7
Expectations of Functions: Let X be distributed over the set N of non-negative integers, with probability...
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