Download 4.2 Random Variables

4-1 and 4-2 Overview and Random Variables
A random variable is a variable that has a single numerical value, determined
by chance, for each outcome of a procedure.
A probability distribution is a graph, table, or formula that gives the
probability for each value of the random variable.
Requirements for a Probability Distribution:
1.  P(x)  1 where x assumes all possible values of x.
2. 0  P( x)  1 for each individual value of x
Determine whether the following is a probability distribution.
1.
3.
X
0
1
2
3
4
5
x
0
1
2
3
4
5
P(x)
.243
.167
.213
.149
.232
.164
P(x)
.309
.232
-.092
.245
.153
.153
2.
X
0
1
2
3
4
P(x)
.4096
.4096
.1536
.0256
.0016
Calculating the mean, variance and standard deviation for a probability
distribution.
µ =  [x • P(x)]
2 =  [(x – µ)2 • P(x)]
2 = [ x2 • P(x)] – µ 2
Mean
Variance
Variance (shortcut)
  [ x 2  P( x)]   2
Standard Deviation

The random variable x is the number of houses sold by a realtor in a
single month.
Houses
Sold
(x)
Probability
0
1
2
3
4
5
6
7
Total
.24
.01
.12
.16
.01
.14
.11
.21
P(x)
x  P (x)
x2
x 2  P( x)
Use the range rule of thumb to find the maximum and minimum values.
Using probability results to Determine When Results are Unusual
 Unusually high: x successes among n trials is an usually high number of
successes if P(x or more) is very small ( such as .05 or less)
 Unusually low: x successes among n trials is an usually low number of
successes if P(x or fewer) is very small ( such as .05 or less)
P(selling 1 or fewer houses) = P(1) + P(0)
Is this unusually low?
P(selling 6 or more houses) = P(6) +p(7)
Is this unusually high?