Interesting Question

Thanks to Xiayang for raising so many exciting questions. I had a lot of fun trying to solve these problems. =)

Problem 1

Usually we get free talking time for our cellphone plan, for example 700 min/month. However, we are always over charged because any incomplete minute will run up to one minute. Meaning that if we dial a number and simply say "Hi" which only takes 2 seconds, on the cellphone bill, it will be reflected as one minute.

(I remember M1 had a policy that they will only run up to a minute when you past 12 seconds of that minute, though I am not quite so sure about it.)

Anyway, the question is, if our call time (in seconds) each time follows a distribution with density function f, what is the expected time that you will see on your phone bill?

This should not be hard if a specific distribution is given, I wrote a short R program to get the expected value. But Xiayang is asking for an answer to the general case, which is pretty hard mathematically.

to put it simply:

Secondsi = time (in seconds) of the ith call made
Given Seconds~i.i.d. f
What is the value of E(ceiling(Seconds/60))

What's hard is the ceiling function is not continuous...

Labels: Sexy Stats

posted by panda xuan @ 11:53 PM