Download Probability Density Curves

Daniel S. Yates
The Practice of Statistics
Third Edition
Chapter 7:
Random Variables
Copyright © 2008 by W. H. Freeman & Company
Probability Histogram can be used to display the probability distribution of a
discrete random variable.
Probability distribution of digits in table of random digits
Probability Distribution of Grades
0=F
1=D
2=C
3=B
4=A
Ex. What is the probability distribution of the discrete random variable X, that is the sum
of a pair of dice.
X can take on values {2,3,4,5,6,7,8,9,10,11,12}
P(X=2) = 1/36 = 0.028
P(X=8) = 5/36 = 0.139
P(X=3) = 2/36 = 0.056
P(X=9) = 4/36 = 0.111
P(X=4) = 3/36 = 0.083
P(X=10) = 3/36 = 0.083
P(X=5) = 4/36 = 0.111
P(X=11) = 2/36 = 0.056
P(X=6) = 5/36 = 0.139
P(X=12) = 1/36 = 0.028
P(X=7) = 6/36 = 0.167
Ex. Probability
density curve
Probability Density Curves
• Any individual value has zero probability
• Only intervals between numbers have probability
• Therefore, P(X>a) and P(X>a) are equal
• Area under probability density curve equals 1
• The normal distribution is a probability density curve
Ex.
7.2 Means and Variances of random variables
Ex. Find the mean size of an American household
Inhabitants
1
2
3
4
5
6
7
Proportion
of
households
0.25
0.32
0.17
0.15
0.07
0.03
0.01
mx = (1)(0.25) + (2)(0.32) + (3)(0.17) + (4)(0.15) + (5)(0.07) +(6)(0.03) +
(7)(0.01) = 2.6