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                              Electrical Engineering and Computer Science             Lecture 6.          Flash and JavaScript are required for this feature.                           . Discrete Random Variables: Consider our coin toss again. 0000032160 00000 n
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  EXAMPLE: Cars pass a roadside point, the gaps (in time) between successive cars being exponentially distributed.          Types of random variable Most rvs are either discrete or continuous, but • one can devise some complicated counter-examples, and • there are practical examples of rvs which are partly discrete and partly continuous. With more than 2,400 courses available, OCW is delivering on the promise of open sharing of knowledge. an example of a random variable. ��Rz3��60�k�-�>$����. stream 0000022155 00000 n
 6 0 obj If we defined a variable, x, as the number of heads in a single toss, then x could possibly be 1 or 0, nothing else.      <>                 » (b) Find a joint pmf assignment for which X and Y are not independent, but for which X2 and Y 2 are independent. 0000048072 00000 n
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                > Download from Internet Archive (MP4 - 28MB), Joint Probability Mass Function (PMF) Drill 1, > Download from Internet Archive (MP4 - 57MB).      Knowledge is your reward. Modify, remix, and reuse (just remember to cite OCW as the source. Hence the two variables have covariance and correlation zero. DISCRETE RANDOM VARIABLES 109 Remark5.3. Such a function, x, would be an example of a discrete random variable.                 »           0000010064 00000 n
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                 » This is one of over 2,200 courses on OCW.      crete random variable while one which takes on a noncountably infinite number of values is called a nondiscrete random variable. Use OCW to guide your own life-long learning, or to teach others. "ϝ/�Vj�ə����V0m� �i&�b�h��"lXz����s��X��9��OJ�݃�?^cqR�Z旤#l��e�4��6o"7U�	UFI'7�c 5Y�Y+ݍ=a�0���դ"P�M���������Eq 0000063790 00000 n
 Made for sharing. Discrete Probability Distributions Let X be a discrete random variable, and suppose that the possible values that it can assume are given by x 1, x 2, x 3, .             Courses (a) Find a joint probability mass assignment for which X and Y are independent, and conflrm that X2 and Y 2 are then also independent. S�{��T���7�_���aLA 
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                Review the tutorial problems in the PDF file below and try to solve them on your own. m�XF�+�m`����Il��.��5OR�栛Q� �`I!�#��f%2��~\\v%���Z\�O1� :9 1�}~�����q�HY�zᅯ��8�rx�0D1��i�������^[즨��`ُ\��VNs&{k�K'z�ﱉ�6�+�-�\��6=�[�������g���a���'&m�Ho���p��	��'{����6���"�';X��CΨ0��u�'9�>���"~X��b��3YE�XPx,����%��)$+�U�P�`	I�$�tw������_�.�VP�c0�u��6P���'�E��|���@6�uvz;�����02H�/�Yم�`�퉵�"D�{����ȕRڔ3��p�?              �ŷMd��.P����d�v�r˿��ѹX�mR�LN@��>Վdep��XOd_��HN�¢�z�̅T �?���4�ħ���{���*�/�Ź��p�0Kr�P �2C�Y9 ��A�20�ݻ�����*���5'�����2ʖ37Ѽ(é�?�j*0fT���&m,�w��&�c��E  �}y�
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 Example 6-3: Consider the coin tossing experiment with S = {H, T}. The characteristics of a probability distribution function (PDF) for a discrete random variable are as follows: Each probability is between zero and one, inclusive (inclusive means to include zero and one). %PDF-1.2
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 We could have heads or tails as possible outcomes. Freely browse and use OCW materials at your own pace. Review the Lecture 6: Discrete Random Variable Examples; Joint PMFs Slides (PDF) Read Sections 2.4–2.6 in the textbook; Recitation Problems and Recitation Help Videos. 0000065046 00000 n
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 Your use of the MIT OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use. No enrollment or registration. 15.063 Summer 2003 1616 Continuous Random Variables A continuous random variable can take any value in some interval Example: X = time a customer spends waiting in line at the store • “Infinite” number of possible values for the random variable. Two of the problems have an accompanying video where a teaching assistant solves the same problem.                      
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