Suppose X1;X2 are two independent geometrically
distributed random variables whose parameters are respectively 1/2 and 1/3 : What
is P(X1 = X2)?
It seems to me that P(X1 = X2)= sum(x=0..+oo) P(X1 = x AND X2 = x)
Since X1 and X2 are i.i.d, P(X1 = x AND X2 = x) = P(X1 = x) P(X2 = x)
Now, substituting the expressions for each probability above you should be done
It seems to me that P(X1 = X2)= sum(x=0..+oo) P(X1 = x AND X2 = x)
Since X1 and X2 are i.i.d, P(X1 = x AND X2 = x) = P(X1 = x) P(X2 = x)
Now, substituting the expressions for each probability above you should be done
summation(x=0..+oo) [P(X1 = x AND X2 = x)]
=p(x1=0,x2=0)+ p(x1=1, x2=2)+p(x1=3,x2=3).....
=p(x1=0)p(x2=0)+ p(x1=1)p(x2=1)+......
where p(x1=x)=(1/2)( (1-1/2)^x);p(x2=x)= (1/3)( (1-1/3)^x)<--am i right here??