Lecture3_Chap3Pt1

Lecture3_Chap3Pt1 - Chapter3Part1 DiscreteRandomVariables...

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Chapter 3 Part 1 Discrete Random Variables and Special Distributions
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Random Variables Our book – A random variable is a real- valued function whose domain is the sample  space. The probability distribution of a random  variable is defined by the numerical values,  and their probabilities, associated with a  certain random experiment. 
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Two Types of Random  Variables Discrete – Random variables taking values  that can be put in a one-to-one  correspondence with the integers.  There are  gaps between the values they can take.   The number on which a six-sided die lands. Continuous – Random variables taking values  on an interval of values.     Distance traveled to school.
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Notation We use capital letters to refer to random  variables.  For instance X, Y, or Z.  We use  lower case letters to refer to any particular  result or realization of a random variable.  For  instance x, y, and z.   (Y=y) refers to the set of all points in the  sample space, S, assigned the value y by the  random variable Y.
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Probabilities We write the P(Y=y) as p(y).  It is the sum of  the probabilities of all sample points in S that  are assigned the value y. The list of probabilities for all values of y is  known as the probability distribution of Y Remember!  All probabilities sum to one!
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Discrete Example One A fair six-sided die is rolled.  We record  the remainder of the result when it is  divided by four. What is the Sample Space? Which values does Y take? What is the probability distribution of Y?
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Work S =  Y =  y p(y) 1
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Discrete Example 2 The number of viruses lurking about the  water fountain at a nameless high  school are known to range anywhere  from 1 to infinity.  The probability that  there is i bacteria is one half raised to  the ith power.  Answer the questions from Example  One
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Work S =  Y =  y p(y) 1
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This note was uploaded on 10/01/2009 for the course STA 505 taught by Professor Lisamarano during the Spring '09 term at West Chester.

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Lecture3_Chap3Pt1 - Chapter3Part1 DiscreteRandomVariables...

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