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# If set x has elements how many elements do p x has how many elements of p x are proper

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his year. I'm looking for a formula that will tell me the probability that a person will cough x number of times in a given week. I started with the Poisson Distribution, but Poisson doesn't seem to take into account standard deviation. To calculate the probability with Poisson, only the mean, expected value, and test value are needed, meaning the variance/standard deviation of the data could vary widely, and you'd still get the same probability distribution. For example, if someone coughed exactly 5 times everyday, you'd get the same probability distribution if this person alternated coughing 0 times one day, 10 times the next, 0 times the next day, 10 times the next, and so on. Does my question make sense? Thanks for your help.
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