STAT 245 Lecture Notes - Lecture 4: Random Variable, Standard Deviation
STAT 245.3 – Exercises #4
Solutions
PROBLEM A: Records kept by Health and Welfare Canada suggest the following probability
distribution of the number of children for families in which the couples have been married at least
eight years.
Number of Children
0
1
2
3
4
5
Probability
0.13
0.24
0.34
0.15
0.09
0.05
Let X be a random variable that denotes the number of children in a randomly selected family in
which the couple has been married at least eight years.
Expand the above table as shown in the examples in your lecture notes. Where calculations are
necessary, practice showing details of your work in arriving at answers to the following problems.
1. What is the probability that such a randomly selected family has fewer than three children?
2. Determine
3XP
.
OR
To answer the following questions, we expand the above probability distribution table:
Number of
children, X
0
1
2
3
4
5
Sum,
∑
Probability,
0.13
0.24
0.34
0.15
0.09
0.05
1
0
0.24
0.68
0.45
0.36
0.25
1.98
1.98
0.98
0.02
1.02
2.02
3.02
3.9204
0.9604
0.0004
1.0404
4.0804
9.1204
0.509652
0.230496
0.000136
0.156060
0.367236
0.456020
1.7196
0
0.24
1.36
1.35
1.44
1.25
5.64
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Document Summary
Problem a: records kept by health and welfare canada suggest the following probability distribution of the number of children for families in which the couples have been married at least eight years. Let x be a random variable that denotes the number of children in a randomly selected family in which the couple has been married at least eight years. Expand the above table as shown in the examples in your lecture notes. Where calculations are necessary, practice showing details of your work in arriving at answers to the following problems: what is the probability that such a randomly selected family has fewer than three children, determine. To answer the following questions, we expand the above probability distribution table: (cid:4666)
