0
Still curious? Ask our experts.
Chat with our AI personalities
Lao
Taiga
BeauAdd your answer:
Earn +20 pts
What does sdf stand for?
5 dollar love me long time?
How many hundreds are there in hundred thousand?
There are 1000 100s in 100,000
How do you know x bar and R charts follow normal distribution?
Central Limit Theorem
What is hyper-geometic probability?
The hyper-geometric distribution is a discrete probability distribution which is similar (in some respects) to the binomial distribution. Suppose you have a population of N which contains R successes. The Binomial describes the probability of r successes in n draws out on N with replacement.However, in many situations the draw is not replaced. In this case you get the hyper-geometric distribution.The function is given by:Prob(r successes in n draws out of N) = RCr/[N-RCn-r * NCn]With the binomial distribution the probability of success remains constant (=R/N) throughout. With the hypergeometric, the numerator for success reduces by one after each successful outcome whereas the denominator reduces by one whatever the outcome.
Why is it said that poisson distribution is a limiting case of binomial distribution?
This browser is totally bloody useless for mathematical display but...The probability function of the binomial distribution is P(X = r) = (nCr)*p^r*(1-p)^(n-r) where nCr =n!/[r!(n-r)!]Let n -> infinity while np = L, a constant, so that p = L/nthenP(X = r) = lim as n -> infinity of n*(n-1)*...*(n-k+1)/r! * (L/n)^r * (1 - L/n)^(n-r)= lim as n -> infinity of {n^r - O[(n)^(k-1)]}/r! * (L^r/n^r) * (1 - L/n)^(n-r)= lim as n -> infinity of 1/r! * (L^r) * (1 - L/n)^(n-r) (cancelling out n^r and removing O(n)^(r-1) as being insignificantly smaller than the denominator, n^r)= lim as n -> infinity of (L^r) / r! * (1 - L/n)^(n-r)Now lim n -> infinity of (1 - L/n)^n = e^(-L)and lim n -> infinity of (1 - L/n)^r = lim (1 - 0)^r = 1lim as n -> infinity of (1 - L/n)^(n-r) = e^(-L)So P(X = r) = L^r * e^(-L)/r! which is the probability function of the Poisson distribution with parameter L.
