Suppose I have a website where people buy something and I've measured the conversion (calculated as buyers / visitors), and it's 0.05.

I want to know what the probabilities are for the different numbers of purchases by the next 100 visitors.

Is it correct to look at it as the probability density function of a binomial distribution where n=100 and p=0.05?

PDF plotted in Mathematica

For example, the probability of having exactly 4 purchases would be 0.178143 in this case.

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    $\begingroup$ The two necessary conditions for a binomial distribution are that each trial (in this case customer) has an identical probability and that the trials are independent from one another. I don't know the specifics of the data, but I could imagine the argument that these requirements are satisfied after say conditioning on customer demographic and profile information and unique customer. If the next 100 customers contain some of the same customers as the last, these groups are unlikely to be independent for example. glm with FE or RE or bayesian heirarchical model could work well.. $\endgroup$ – Tyrel Stokes Aug 26 '20 at 17:42
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    $\begingroup$ If the customer mix between the n=100 batches are well mixed, then the model you described will approximate well the more complicated model I described at the bernoulli level. If you believe this to be the case, it would be reasonable to model directly as an unconditional binomial, but I would be careful to check those simplifying assumptions $\endgroup$ – Tyrel Stokes Aug 26 '20 at 17:43
  • $\begingroup$ Yes, let's assume there are no repeated customers in the next 100 so the groups are independent and let's assume they are well mixed. $\endgroup$ – user7817 Aug 27 '20 at 10:15
  • $\begingroup$ Can a single buyer make more than one purchase? If that were the case, the independence assumption might be doubted. $\endgroup$ – F. Tusell Mar 13 at 8:22

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