MATH 533 Final Exam 2021

1. a) What is the difference between discrete and continuous random variables?
A continuous random variable is one which takes an infinite number of possible values.
A discrete random variable is one which may take on only a countable number of distinct 
values such as 0, 1, 2, 3, 4, ... Discrete random variables are usually (but not necessarily) 
counts.
b) Give two examples of each.
Example Continuous Random Variables:
1. The amount of sugar in an apple.
2. The time required to run a mile.
Example Discrete Random Variables:
1. The number of children in a family.
2. The Sunday night attendance at a Church.
2. Find each of the following:
a) z.90 0.1841 
b) z.85 0.1977 
c) z.05 0.4801 
d) z.01 0.496 
3. Suppose that in a certain population, 95% of the people are free of a certain disease and 
5% of the population has the disease. Suppose further that a test for the disease yields a 
positive result 99% of the time if the subject has the disease but yields a positive result 
10% of the time when the subject does not have the disease. If a subject’s test results are 
positive, what is the probability that they have the disease?
a) 99% 
b) 100% 
c) 90.8% 
d) 89.5% 
4) If X is N(5, 2), find: