We observe X Dell computers breaking down out of 10 in an office. We do not know the value of pi (the proportion of computers that break down for this brand). We know that the probability distribution for the random variable X is binomial, with parameters n=10 and pi. We want to explore a statistical/mathematical motivation for using p (the sample proportion) to estimate pi in this situation.
Write down the probability mass function (pmf = Pr(X=x) = f(x)) for the random variable X. Let n=10 in your answer, but leave pi as a symbol since it is not know.
I have idea how a probability mass function should look like. I know that a pmf for a 6 sided fair die is f(u) = 1/6 for u=1,2,3,4,5,6. Similarly, I know that if we have some sort of different phenomenon, the probabilities could be different and we have f(u) = 1/100 for u=1 , 5/100 for u=2, ..., ?/100 for u=n... as long as all sum up to 100/100. I think is something similar to what I have here. I'm just not sure how to implement the pi into the pmf. I know pi is the mean. Please assist.