poisson distribution question (FS1)

[limpid mountain]

why cant u just work it out normally? why do they create a new variabl e

[main hearth]

I think an approximation is only appropriate when n is large and p is small

[limpid mountain]

oh fait enough

[hallow vault]

yup

[simple lily]

Rule of thumb is np < 10 is appropriate

But if u used probability 0.95 then it would be way above that

[hallow vault]

yeah although for actual exam qs dont strictly stick to that since you'll be asked to use poisson approximations even though most the time np > 10

[simple lily]

Really

I haven’t seen exam qs with np > 10

And if they do they usually have a part which says why is a poisson approximation not suitable

[hallow vault]

yeah for example Q3b here

but well it still works out bc n is large and p is very small

but yeah like sometimes u might get questions asking something like: "explain whether or not Po(4) is a good approximation to B(10,0.4)" and you wouldn't get marks for talking about the "np<=10" rule,
you'd just need to state "n is large and p is small therefore suitable" or vice versa

[hallow vault]

its all good tho since like u said the q will always tell u when u should use a poisson approximation

sometimes they dont but you can figure it out pretty easily or at the last part it'll say "explain why a poisson approximation is unsuitable" which kinda is a spoiler alert that you need to use poisson for the previous parts

[simple lily]

This is more of a scaling up question

U scale up the lambda value to match the time period

I haven’t seen many explicit “use a poisson approximation” questions with np greater than 10

Where they give u information to build a binomial distribution and u have to use poisson

In this case they’ve just given u poisson information and u need to scale ur lambda value to the new time period

So just 2.4 x 8

Since ur going from 1hr to 8hrs

[hallow vault]

oh yeah u r right its not an approximation its just poisson

i remember a q with np>10 w/ approximation but i cant find it they r prolly uncommon