Question

The number of pages in a PDF document you create has a discrete uniform distribution from five to nine pages (including the end points). What are the mean and standard deviation of the number of pages in the document ?

Answer 1

Let X = the random variable denoting the number of pages in the PDF document that has been created

Then we have,

X ~ Uniform{a, b}, a and b are the parameters of the distribution

Now, the expectation and variance of X are given by,

E(X) = $\frac{a+b}{2}$

and Var(X) = $\frac{(b-a+1)^2-1}{12}$

Here we are given,

a = 5, b = 9

Using these values we get,

E(X) = $\frac{5+9}{2}=7$

and Var(X) = $\frac{(9-5+1)^2-1}{12}=2$

Then standard deviation of X = $\sqrt{Var(X)}=\sqrt{2}=1.414$ (rounded to 3 decimal places)

Answer: The mean and standard deviation of the number of pages in the document are 7 and 1.414 respectively.