.. title: Engineering Probability Class 9 Thurs 2018-02-15
.. slug: class09
.. date: 2018-02-15
.. tags: mathjax
.. category: class
.. link: 
.. description: 
.. type: text

.. sectnum::
.. contents:: Table of contents
..



Homework 1-3 solutions
----------------------

#. https://docs.google.com/document/d/1TPQIZpP6F4TbZZy4aU_damf5eEy8F4vQx0KOS3yP7NU/edit?usp=sharing
#. https://docs.google.com/document/d/1rt3ahzZy-wYaycr3ZCts2UHI7Ik68X3QJjtZxCTVva8/edit?usp=sharing
#. https://docs.google.com/document/d/1mMLkUCW4lLvNj7UeWRlKWP906V7hxgr0-Wg1ySM9Ncw/edit?usp=sharing


Chapter 3 ctd
-------------


#. Example 3.22 Variance of geometric r.v.
   We'll derive it.

#. Example 3.24 Residual waiting time
   
   #. X, time to xmit message, is uniform in 1...L.
   #. If X is over m, what's probability that remaining time is j?
   #. :math:`p_X(m+j|X>m) = \frac{P[X =m+j]}{P[X>m]} = \frac{1/L}{(L-m)/L} = 1/(L-m)`

#. :math:`p_X(x) = \sum p_X(x|B_i) P[B_i]`

#. Example 3.25 p 113 device lifetimes
   
   #. 2 classes of devices, geometric lifetimes.
   #. Type 1, probability :math:`\alpha`, parameter r.  Type 2 parameter s.
   #. What's pmf of the total set of devices?

#. Example 3.26.

#. 3.5 More important discrete r.v

#. Table 3.1: We haven't seen :math:`G_X(z)` yet.

#. 3.5.4 Poisson r.v.
   
   #. The experiment is observing how many of a large number of rare events happen in, say, 1 minute.  
   #. E.g., how many cosmic particles hit your DRAM, how many people call to call center.
   #. The individual events are independent.
   #. The r.v. is the number that happen in that period.
   #. There is one parameter, :math:`\alpha`.  Often this is called    :math:`\lambda`.

      .. math::
	 
	 p(k) = \frac{\alpha^k}{k!}e^{-\alpha}
	 
   #. Mean and std dev are both :math:`\alpha`.
   #. In the real world, events might be dependent.   

Material added after class
--------------------------

#. `My handwritten tablet notes <../../handwritten/215.pdf>`_.