.. title: Engineering Probability Class 18 Mon 2018-03-26
.. slug: class18
.. date: 2018-03-26
.. tags: mathjax
.. category: class
.. link: 
.. description: 
.. type: text

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

Exam 2, Thurs 3/29 
-------------------

Summary
=======

#. Closed book but a calculator and two 2-sided letter-paper-size note sheets are allowed.
#. Material is mostly from chapter 4, with maybe some from chapters 1-3.
#. Questions will be based on book, class, and homework, examples and exercises.
#. The hard part for you may be deciding what formula to use.
#. Any calculations will (IMHO) be easy.
#. Speed should not be a problem; most people should finish in 1/2 the time.

Material on exam
================

#. distributions:

   a. uniform: discrete, continuous
   #. exponential:  This is the interarrival time between i.i.d (indep and identically distributed) events, e.g., radioactive decays, or web server hits.

   #. normal
 
   #. Poisson:  This is the probability distribution for the number of events in a fixed time, when each possible event is independent and identically distributed.

      Examples:

      i. number of atoms decaying in a block of radium.
      #. number of hits on your web server.
      #. number of students visiting bursar.

   #. binomial
   #. Bernoulli
   #. Geometric

   For each distribution: pdf/pmf, cdf, mean, variance.  (Pages 116, 164).

#. I might give you a new pdf and ask you to compute the cdf.

#. conditional probabilities.

#. Markov and Chebyshev inequalities.

#. function of a r.v.

#. Reliability.  R(t) = 1-F(t).

#. MTTF (new)  p 190.

   MTTF = $\\int_0^\\infty R(t) dt$

   Ex. MTTF of U[0,1].

#. Failure rate.

   r(t)dt is the probability of failing in the next dt.

   $$r(t) = \\frac{-R'(t)}{R(t)}$$

   Ex: do on U[0,1].

#. Reliability.  

#. pdf/cdf of the max/min/sum of 2 r.v.


Material not on exam
====================

#. characteristic functions.

#. moment generating functions.

#. Matlab.
   
#. entropy.

#. generating random variables.

#. Chi-square

#. Weibull.


An old exam
-----------

https://wrf.ecse.rpi.edu/pmwiki/pmwiki.php/EngProbSpring2011/Exam2

Answers: https://wrf.ecse.rpi.edu/pmwiki/pmwiki.php/EngProbSpring2011/Exam2Sol

Normal Q function
-----------------

`Table <http://www.ece.ucdavis.edu/~levy/eec161/qfunc.pdf>`_ from UD Davis E&CE411, Spring 2009.


Iclicker questions
------------------

#. Consider a fair tetrahedral die, with faces labeled 1, 2, 3, 4.  What is f(2)?

   a. 1/6.
   #. 1/4.
   #. 1/2.
   #. 0.
   #. 1.
     
#. For the same die, what is F(2)?

   a. 1/6.
   #. 1/4.
   #. 1/2.
   #. 0.
   #. 1.   

#. Consider the continuous distribution with f(x) = $x^2$  for $0\\le x \\le \\sqrt[3]{3}$.   What is F(x)?

   a. $x$
   #. $x^2$
   #. $x^3$      
   #. $x^2/2$
   #. $x^3/3$

#. For that distribution, what is F(1)?

   a. 0
   #. 1/3
   #. 1/2
   #. 1
   #. None of the above.

#. For the uniform U[0,2] distribution, what's the reliability R(1/2)?

   a. 1/2
   #. 1/4
   #. 3/4
   #. 1
   #. None of the above.

#. For that distribution, what's the failure rate at 1/2?

   a. 1/2
   #. 1/4
   #. 3/4
   #. 1
   #. None of the above.

 
      
         

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

#. `My handwritten tablet notes <../../handwritten/326.pdf>`_.