Thread: hypergeometric distibution

I just need some help on where to get going with this because i tried but cant seem where to go!!!

Show that the hypergeometirc p.m.f given by P(x=K)= (r choose k)(N-r choose n-k)/(Nchoose n)
will converge to the binomial distirubtion (n choose k)p^k(1-p)^n-k if N=pr and N approcrahes infinity

I was thinking of rearranging N to to obtain r=N/p and then puttin that into teh p.m.f but im not sure whether this the right pathway???

Originally Posted by calculusgeek

I just need some help on where to get going with this because i tried but cant seem where to go!!!

Show that the hypergeometirc p.m.f given by P(x=K)= (r choose k)(N-r choose n-k)/(Nchoose n)
will converge to the binomial distirubtion (n choose k)p^k(1-p)^n-k if N=pr and N approcrahes infinity

I was thinking of rearranging N to to obtain r=N/p and then puttin that into teh p.m.f but im not sure whether this the right pathway???

Read this: The Hypergeometric Distribution

Part 20 is the relevant bit.

thank for your help, i have tried doing that but is it a thing where i have to subst pr for N in teh hypergeometirc distribution and then work my way thorugh that or do i subst in teh binomial dist to show the hypergeometric

i tried to the first however when trying to evalute the binomial coffiencts to see if r factors os i can cancel them out i get into a big fat mess so im unsure if thsi is the right way

also if N approaches infinity since R/N apporcahes p doesn't p alos approcah infinity