(New page: == Instructions == Homework 6 can be [https://engineering.purdue.edu/ece302/homeworks/HW6FA08.pdf downloaded here] on the [https://engineering.purdue.edu/ece302/ ECE 302 course website]. ...) |
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Homework 6 can be [https://engineering.purdue.edu/ece302/homeworks/HW6FA08.pdf downloaded here] on the [https://engineering.purdue.edu/ece302/ ECE 302 course website]. | Homework 6 can be [https://engineering.purdue.edu/ece302/homeworks/HW6FA08.pdf downloaded here] on the [https://engineering.purdue.edu/ece302/ ECE 302 course website]. | ||
| − | == Problem 1: | + | == Problem 1: Ceiling of an Exponential == |
| + | <math>X</math> is an exponential random variable with paramter <math>\lambda</math>. <math>Y = \mathrm{ceil}(X)</math>, where the ceiling function <math>\mathrm{ceil}(\cdot)</math> rounds its argument up to the closest integer, i.e.: | ||
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| + | What is the PMF of <math>Y</math>? Is it one of the common random variables? (Hint: for all <math>k</math>, find the quantity <math>P(Y > k)</math>. Then find the PMF) | ||
Revision as of 08:16, 8 October 2008
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.:
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)
