Illinois Institute of Technology
Department of Applied Mathematics
Math 100
Homework Assignment
Due Monday, November 19, 2007
1. Consider flipping 3 coins. Describe Ω - the sample space. Find some sets (events)
A, B from Ω, such that A, B are dependent.
2. A family has two children. What is the probability that both are boys, given
that at least one is a boy?
(Hint: the chances that one child is a Boy or a Girl is .5)
3. Suppose that the number of typographical errors on a single page of a given book
has a Poisson distribution with parameters λ=1
2. Find the probability that
there are at least two errors on page #10 (the book has more than 10 pages).
4. An urn contains Nwhite and Mblack balls. Balls are randomly selected, one at
a time, with replacement, until a black one is obtained. What is the probability
that exactly ndraws are needed.
(Hint: use Geometric(p). the problem is to guess p)
5. Find the mean and variance of Uniform(0,1).
6. Give a real-life example of a random variable with Uniform distribution.
7. Run the applet from http://www.stat.sc.edu/~west/javahtml/CLT.html. Explain in words
what is the CLT about.
8. (Extra) pin (1) from the slides stands for probability of the coin coming up H
or T. Which one?
Hint: you do not have to solve the entire problem from the very beginning, just
think what this formula means.
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