.. title: Engineering Probability Class 25 Thurs 2021-04-29
.. slug: class25
.. date: 2021-04-29
.. tags: class
.. link: 
.. description: 
.. type: text
.. has_math: true

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


Webex
-----

I'll have 2 laptops and an ipad for today's class.  We'll see what works.


Worked out examples and problems
--------------------------------

perhaps some of these.


#. 5.33, p 267

#. ex 7.1 p360

#. Section 7.2, p365.

   Note: Chebyshev inequality, Eqn 4.76, p 182. says

   :math:`P[ | X-m | \ge a ] \le  \sigma^2/ a^2`

   Eqn 7.20, p 366 is useful:

   :math:`P[ | M_n-\mu | < \epsilon ] \ge 1 - \sigma^2 / (n \epsilon^2)`

#. Example 7.10, 7.11, 7.12.	 
   
#. 7.14a, p 403.

#. 8.3 p 471.
   
#. 8.4 p 471.

   Normal probability tables were given in class 20. 

#. 8.10, p 472.

::
#. 8.24, p 474.


Useful tables
-------------

   TABLE 3.1 Discrete random variables is page 115.

   TABLE 4.1 Continuous random variables is page 164.


Normal distribution table
-------------------------

For your convenience.   I computed it with Matlab.::

   x          f(x)      F(x)      Q(x)
   -3.0000    0.0044    0.0013    0.9987
   -2.9000    0.0060    0.0019    0.9981
   -2.8000    0.0079    0.0026    0.9974
   -2.7000    0.0104    0.0035    0.9965
   -2.6000    0.0136    0.0047    0.9953
   -2.5000    0.0175    0.0062    0.9938
   -2.4000    0.0224    0.0082    0.9918
   -2.3000    0.0283    0.0107    0.9893
   -2.2000    0.0355    0.0139    0.9861
   -2.1000    0.0440    0.0179    0.9821
   -2.0000    0.0540    0.0228    0.9772
   -1.9000    0.0656    0.0287    0.9713
   -1.8000    0.0790    0.0359    0.9641
   -1.7000    0.0940    0.0446    0.9554
   -1.6000    0.1109    0.0548    0.9452
   -1.5000    0.1295    0.0668    0.9332
   -1.4000    0.1497    0.0808    0.9192
   -1.3000    0.1714    0.0968    0.9032
   -1.2000    0.1942    0.1151    0.8849
   -1.1000    0.2179    0.1357    0.8643
   -1.0000    0.2420    0.1587    0.8413
   -0.9000    0.2661    0.1841    0.8159
   -0.8000    0.2897    0.2119    0.7881
   -0.7000    0.3123    0.2420    0.7580
   -0.6000    0.3332    0.2743    0.7257
   -0.5000    0.3521    0.3085    0.6915
   -0.4000    0.3683    0.3446    0.6554
   -0.3000    0.3814    0.3821    0.6179
   -0.2000    0.3910    0.4207    0.5793
   -0.1000    0.3970    0.4602    0.5398
         0    0.3989    0.5000    0.5000
    0.1000    0.3970    0.5398    0.4602
    0.2000    0.3910    0.5793    0.4207
    0.3000    0.3814    0.6179    0.3821
    0.4000    0.3683    0.6554    0.3446
    0.5000    0.3521    0.6915    0.3085
    0.6000    0.3332    0.7257    0.2743
    0.7000    0.3123    0.7580    0.2420
    0.8000    0.2897    0.7881    0.2119
    0.9000    0.2661    0.8159    0.1841
    1.0000    0.2420    0.8413    0.1587
    1.1000    0.2179    0.8643    0.1357
    1.2000    0.1942    0.8849    0.1151
    1.3000    0.1714    0.9032    0.0968
    1.4000    0.1497    0.9192    0.0808
    1.5000    0.1295    0.9332    0.0668
    1.6000    0.1109    0.9452    0.0548
    1.7000    0.0940    0.9554    0.0446
    1.8000    0.0790    0.9641    0.0359
    1.9000    0.0656    0.9713    0.0287
    2.0000    0.0540    0.9772    0.0228
    2.1000    0.0440    0.9821    0.0179
    2.2000    0.0355    0.9861    0.0139
    2.3000    0.0283    0.9893    0.0107
    2.4000    0.0224    0.9918    0.0082
    2.5000    0.0175    0.9938    0.0062
    2.6000    0.0136    0.9953    0.0047
    2.7000    0.0104    0.9965    0.0035
    2.8000    0.0079    0.9974    0.0026
    2.9000    0.0060    0.9981    0.0019
    3.0000    0.0044    0.9987    0.0013


x is often called z.

More info: https://en.wikipedia.org/wiki/Standard_normal_table