.. title: Engineering Probability Class 13 Thu 2022-02-24
.. slug: class13
.. date: 2022-02-23
.. tags: class
.. link: 
.. description: 
.. type: text
.. has_math: true

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


TA office hours
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#. Will meet on their webex meeting places.

#. Hao Lu, luh6@, 2pm Tues and 3pm Sat.

#. Hanjing Wang, wangh36@, 3pm Fri and 9pm Sun.

#. If no one has joined in 15 minutes, they will leave.

#. Write them for other meeting times.

   
Homework 6
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is on gradescope.

    

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/>`_