.. title: Engineering Probability Class 15 Thurs 2021-03-18
.. slug: class15
.. date: 2021-03-18
.. tags: class
.. link: 
.. description: 
.. type: text
.. has_math: true

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


No class next Thurs 3/25
------------------------

Attend Pres Jackson's spring town meeting, or sleep late, or go on a hike, or whatever you want.

Homework that was due then is postponed.


Chapter 4, ctd
--------------

#. Example 4.22, page 169.

#. Section 4.4.4 Gamma r.v.

   Setting its 2 parameters to various values gives useful special cases.

   E.g. m-Erlang, the sum of m exponential r.v.

#. Section 4.4.5, Beta r.v., p 173.
      
   Setting its 2 parameters to various values gives useful special cases.

#. Section 4.4.6 Cauchy r.v.

   has no moments.

#. Problem 4.17, p 217.

#. Problem 4.27, p 218.

#. Problem 4.39, p 219.

#. Problem 4.56a, p 220.

#. Problem 4.68, p 222.
      

Chapter 5, Two Random Variables
-------------------------------

#. One experiment might produce two r.v.  E.g.,
   
   #. Shoot an arrow; it lands  at (x,y).  
   #. Toss two dice.
   #. Measure the height and weight of people.
   #. Measure the voltage of a signal at several times.
     
#. The definitions for pmf, pdf and cdf are reasonable extensions of one r.v.
#. The math is messier.
#. The two r.v. may be ***dependent*** and ***correlated***.
#. The ***correlation coefficient***, $\\rho$, is a dimensionless measure of linear dependence.   $-1\\le\\rho\\le1$.
#. $\\rho$ may be 0 when the variables have a nonlinear dependent relation.
#. Integrating (or summing) out one variable gives a marginal distribution.
#. We'll do some simple examples:
   
   #. Toss two 4-sided dice.
   #. Toss two 4-sided ''loaded'' dice.  The marginal pmfs are uniform.
   #. Pick a point uniformly in a square.
   #. Pick a point uniformly in a triangle.   x and y are now dependent.
     
#. The big example is a 2 variable normal distribution.
   
   #. The pdf is messier.
   #. It looks elliptical unless $\\rho$=0.


#. I finished the class with a high level overview of Chapter 5, w/o any math.
   

	
Comic
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`Conditional Risk <https://xkcd.com/795/>`_