In ROSS book《Stochastic Process》page29
there is Example1.5（f）
I want to know why it's rigorous
Pi,n=Pi · P(n-i+1)
the author think the line with n points can be separated as two lines with i
and n-i+1 points.then
Pi,n=Pi · P(n-i+1)
Pi,n stands for the ith point is "isolated point" on the"n points line" Pi stands for the ith point is "isolated point" on the"i points line"
P(n-i+1) stands for the (n-i+1)th point is "isolated point" on the"(n-i+1) points line"
However,I think
the probability of"point pairs" selected on the "n points line"
is different with that
when selected on "i point line" and"n-i+1 point line". because Pi is related to the random selection probability 1/(i-1),which not exist in the problem
So why "Pi,n=Pi · P(n-i+1)"is right?
MANY THANKS!
I'am a student from peking University of China,thanks again. 1 2 3 4 5 6 7 8
