difference between binomial and geometric distribution?

  • 1 vote

I've got in my notes they are both mutually exclusive outcomes and that the binomial is fixed trials but geometric is not fixed trials.. but what do these mean?

Posted Mon 23rd May, 2011 @ 11:36 by Nicola

4 Answers

  • 7 votes

hmmm....both involve failure and success. and all trials are independent.

binomial distribution [X~B(n, p)] has a FINITE number of trials. they'll tell u in the question. for example, it's like 'what is the probability that 3 days out of 7 days are humid days if the prob of a humid day in a city is 0.7?' so you calculate by the formula nCx (p)^x (1-p)^n-x where n=7, x=3 (x is the random variable) and p=prob of success, which is 0.7. E(X)=np while Var(X)=np(1-p)

geometric distribution [X~Geo(p)] is in a sense INFINITE, they're asking you what is the probability UNTIL the first success happens. (that's why it's called 'geometric', as in geometric series), such as

'Paul throws a dice until he gets a '4'. what is the probability of him getting the first '4' in the 6th throw?' you calculate the probability: (1/6)(1-1/6)^5=(1/6)(5/6)^5. general formula: p (1-p)^(X-1). E(X)=1/p; Var (X) = (1-p)/(p^2).

Keep in mind that the events are independent and equally probable. Therefore, if the question asks about drawing balls w/o replacement, these 2 distributions do not apply.

Hope that this can help u.

Answered Tue 24th May, 2011 @ 08:02 by saraht
Edited by saraht on Wed 25th May, 2011 @ 09:07
  • 1 vote

Oh ok, that makes sense saraht, thanks!

So if you have a question asking about w/o replacment, which do you to use to find the answer?

Answered Wed 25th May, 2011 @ 10:05 by Nicola
  • 1 vote

o...if the question is w/o replacement, then there is no model for it...at least I don't know. Then you'll have to use the 'traditional' way, that is the multiplication rule. That's the way I do it.

Answered Wed 25th May, 2011 @ 10:23 by saraht
  • 0 votes

I know of three types of distribution

Normal distribution - 63% approx within 1 standard deviation, 95% within 2 and 99.7% within 3.

Bnomial distribution - one pass, one fail with set probabilities and they are mutually exclusive. In order to work it out you are given outcomes, e.g. (p+q)4 (I can't remember the expansion), and if p=success and q=failure with 4 trials you use this to work out probability of a certain number of successes.

Discrete uniform distribution - when each outcome has the same probability (I think they are mutually exclusive).

I don't know about geometric distribution.

Answered Mon 23rd May, 2011 @ 15:15 by Sarah