Let's say that I have a group of 71 people and I'm trying to find the expected value of how many of their birthdays fall within a specific 6 day time interval (June 12-17).
Would this type of problem work as a binomial random variable? If so, what formula would I use to calculate the expected value? Could I then calculate the variance as well? I know that the formula for the expected value is $P(x) \cdot x$, where $P(x)$ is the chance of success and $x$ is the number of trials.
But I am confused as to whether the 71 people is the number of "trials" and what would the chance of success be? Would it change with each person? Thanks in advance.