Homework6 ECE302Fall2008sanghavi - Rhea

Instructions

Homework 6 can be downloaded here on the ECE 302 course website.

Problem 1: Ceiling of an Exponential

$ X $ is an exponential random variable with paramter $ \lambda $. $ Y = \mathrm{ceil}(X) $, where the ceiling function $ \mathrm{ceil}(\cdot) $ rounds its argument up to the closest integer, i.e.:

        $ \mathrm{ceil}(a) $ = $ a $ if $ a $ is an integer
              = the smallest integer bigger than $ a $ if $ a $ is not an integer

What is the PMF of $ Y $? Is it one of the common random variables? (Hint: for all $ k $, find the quantity $ P(Y > k) $. Then find the PMF)

Problem 2: Fair Wages

Problem 3: An Uncommon PDF

Problem 4: Gaussian Coordinates