4.2 Random Variables

Random Variable  is a variable that has a numeric value for each
                outcome of an experiment
 
 

Examples:

    x  The number of students passing a certain class
 

    x  The number of girls in a family of 5 children
 

    x  The sum on the faces of two rolled die
 

    x  The number of defective parts in a sample of 20
 
 

 Discrete random variable    vs  Continuous random variable

    #2
 

 
    #4
 
 

Probability Distribution   (like relative frequency table)
 
    #6
 

x	P(x)
0	0.0625
1	0.2500
2	0.3750
3	0.2500
4	0.0625

 
     Sum of entries approx. =1,   each entry is valid probability number

     Probability Histogram is like Relative Frequency Histogram pg. 187
 
 
 

Mean, Variance, and Standard Deviation

            Mean 

            Variance   

            Standard Deviation  
 

    **Bad notation in text and on card

    **Round-off rules pg. 190 - one more place than original random variable x

 Work Through #6  above
 
 

   #10    (not a probability distribution because   )
 
 

   #18 -  Number of boys in a family of 3 children
 
 

x	P(x)
0
1
2
3

 
 

Expected Value

    Games of chance, Life insurance ...

                        Expected value 

    #14   
 

	x	P(x)	xP(x)
Win
Lose

 
 
 
 

    #16
 

Prize	P(x)	xP(x)
$5,000,000	1/201,000,000
$150,000	1/201,000,000
$100,000	1/201,000,000
$25,000	1/100,500,000
$10,000	1/50,250,000
$5,000	1/25,125,000
$200	1/8,040,000
$125	1/1,005,000
$89	1/3774