What are the limitations of a binomial distribution?

Question

k the key word is "limitations" dont tell me what a binom distribution is. I want limitations how it is derived, is a better probablity model that binom, like normal distribution. And the first guy who answered the question, do u even know what you are talking about.

Answer 1

If you mean what are the limitations of the applicability of the binomial model, the standard litany is the following:

1) a fixed number of trials, n.
2) trials are independent of each other
3) each trial consists of two outcomes, success or failure
4) the probability of sucess is the same on each trial
5) the binomial random variable is the number of successes on n trials.

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there is no reason to be rude. You are using the word "limitations" in a very nonstandard way. In practice, whenever someone wants to check whether a binomial model is appropriate for a particular application, they go through the checklist I posted to test whether each of the assumptions is valid in the concrete situation to be studied. (In that sense, the applicability of the model is limited!)

For example, if a survey is conducted in which the surveyer simply asks her friends the questions, rather than choosing a random sample, the assumption of independence is violated, and all the calculations based on the binomial formulas will be irrelevant.

the normal and binomial random variables measure different things. It's not a matter of one being better than the other. If I have 30 students and I observe their SAT scores, then those scores might follow a normal distribution. But if I have 30 students and I ask whether or not each one took the SAT, then the responses follow a binomial distribtuion.

check that for yourself: go down my list and you'll see that the criteria I listed are not followed for the first example but might hold for the second.

As for deriving the binomial formula, that is way too long to put here. For your information, the first poster did in fact tell you something relevant for the derivation of the binomial formula. He is referring to the binomial theorem, and he knows what he is talking about.

Answer 2

In (x+y)^n, n should be a positive integer.