Y dosraniad Poisson fel brasamcan i’r Binomial. Pan mae’r nifer y treialon mewn dosraniad Binomial yn fawr iawn, a’r tebygolrwydd i lwyddo yn fach iawn, mae np ~ npq (gan fod q ~ 1), felly mae’n bosib newid y dosraniad i fod yn un Poisson. Brasamcan o’r tebygolrwydd a gawn yn unig. The Poisson distribution as an approximation of the Binomial. When the number of trials in a Binomial distribution is very large, and the probability of success is very small, then np ~ npq (as q ~ 1), therefore it is possible to change the distribution to a Poisson distribution. We will only have an approximation of the probability.

I newid dosraniad o’r Binomial i’r Poisson, rhaid darganfod y cymedr yn gyntaf. X ~ B ( 500, 0.01 ) Cymedr - Mean = np = 500 x 0.01 = 5 Felly’r brasamcan yw Y ~ Po ( 5 ) In order to change from Binomial to the Poisson, we need to calculate the mean. The approximation is therefore Y ~ Po ( 5 )

Enghraifft - Example Mae X yn dynodi nifer y sgriwiau diffygiol mewn paced o 1000 o sgriwiau ac mae ganddo ddosraniad Binomial fel bod X ~ B ( 1000, ) Darganfyddwch y tebygolrwydd fod 2 neu fwy o sgriwiau diffygiol mewn paced. Gan fod X ~ B ( 1000, ) mae Y ~ Po(1000 x 0.003) Y ~ Po(3) P(X ≥ 2)  P(Y ≥ 2) = X is the number of defective screws in a packet of 1000 screws. X has a Binomial distribution X ~ B ( 1000, ) Calculate the probability that 2 or more of the screws are defective. Since X ~ B ( 1000, ), Y ~ Po(1000 x 0.003)

Ymarfer/Exercise 4.7 Mathemateg - Ystadegaeth Uned S1 – CBAC Mathematics Statistics Unit S1 - WJEC Gwaith Cartref/Homework 8 Gwaith Cartref/Homework 9