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?
- 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.
- 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?
- 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.
- 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.