A real number between 0 and l00 is randomly selected according to a uniform distribution and rounded off to the nearest integer.
For example, 36.5001 is rounded off to 37; √3 is rounded off to 2; and 69.49 is rounded off to 69.
Define a random variable to be X = number selected - nearest integer .
(a) What is the domain of this random variable?
(b) Determine the PDF for X .
(c) Determine the mean square value of X .