# Is binomial distribution approriate

• aaaa202
In summary, the probability of getting n 6's when tossing 6 dice with a probability of 1/6 for each die to show a 6 is binomially distributed. However, if the probability for each die to show a 6 increases continuously from 0 to 1/6 over time, the total number of 6's will not have a binomial distribution.
aaaa202
Suppose I have 6 die and toss them. The probability to have n 6's is binomially distributed with parameter 1/6.
Now suppose instead tossing the 6 die and having 1/6 probability for a 6 each dice's probability to show 6 grows continously in the time interval t=0 to t from 0 to 1/6. Can I then say that as before, the probability to have n 6's is binomially distributed with parameter 1/6?

aaaa202 said:
Suppose I have 6 die and toss them. The probability to have n 6's is binomially distributed with parameter 1/6.
Now suppose instead tossing the 6 die and having 1/6 probability for a 6 each dice's probability to show 6 grows continously in the time interval t=0 to t from 0 to 1/6. Can I then say that as before, the probability to have n 6's is binomially distributed with parameter 1/6?

I think I know what you are trying to say, but let me re-word it first. You have 6 dice (not 'die'--a 'die' = one single cube). At any toss they each have the same probability p of showing a '6', but the probability p increases from 0 to 1/6 as we make more tosses. If ##p_k## is the probability of a die showing '6' on toss k, then the number ##N_k## of 6's on toss k is binomial with parameters ##(6,p_k)##. If we finally get a probability of 1/6 on the nth toss (that is, ##p_n = 1/6##), the total number of 6's altogether is ##X = \sum_{k=1}^{n} N_k##. This will NOT have a binomial distribution, because although the summands are independent, they are not identically distributed. In fact, you can easily work out the mean and variance of X and find that they are not related to each other as a binomial would give.

## 1. What is binomial distribution and when is it used?

Binomial distribution is a probability distribution that describes the likelihood of a certain number of successful outcomes in a series of independent trials. It is used when there are two possible outcomes for each trial, and the probability of success remains constant throughout the trials.

## 2. How do I know if binomial distribution is appropriate for my data?

Binomial distribution is appropriate for data that meets the following criteria: 1) there are a fixed number of trials, 2) each trial has only two possible outcomes, 3) the trials are independent of each other, and 4) the probability of success remains constant throughout the trials.

## 3. Can binomial distribution be used for continuous data?

No, binomial distribution is only appropriate for discrete data where there are a fixed number of trials with two possible outcomes.

## 4. What is the difference between binomial and normal distribution?

The main difference between binomial and normal distribution is that binomial distribution is used for discrete data with a fixed number of trials and two possible outcomes, while normal distribution is used for continuous data with a bell-shaped curve.

## 5. Is there a specific formula for calculating binomial distribution?

Yes, the formula for calculating binomial distribution is: P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, x is the number of successful outcomes, p is the probability of success, and q is the probability of failure (1-p).

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