What are the mean and standard deviation of the probability density function given by #(p(x))/k=(1-1/(1-x))# for # x in [2,10]#, in terms of k, with k being a constant such that the cumulative density across the range of x is equal to 1?
First, let's rewrite the PDF (probability density function) as follows:
(the PDF is always 0 outside of the range of
We will use the formula for the
The mean is the first moment (simply put
Now, to find the standard deviation, we'll first evaluate the variance form the following formula:
This is how it looks in terms of