Homework #10 for 445
Due: March 27, 2006
Read Chapters 7,8 of Meerschaert.
Exercises from the text (Meerschaert)
1. Section 7.4, Problem 7. For part b) assume that there is only one winning number per week.
2. Section 7.4, Problem 6. For part a). It may be helpful to use the fact that
∞
X
zn
= ez
n!
n=0
.
For part c), use the exact probability density function for Poisson r.v.’s to find the 95% confidence interval around the mean. Do not use the normal approximation. In part d) you will
compare with the normal approximation given in the book.
3. Section 8.4, Problem 16.
There will be no class on Friday, March 25. Insteady of class, do the following exercise:
4. a) Generate a sequence of n uniform random variables, with density defined over the interval
[0, 1]. You can generate this sequence of random variables using rand in Matlab. Use this
sequence of random variables to construct several histograms which use different sized intervals
(bins). You can use the Matlab function hist to construct a histogram. Compare with the exact
probability density function for these random variables. Try this for several different values of
n large. Do you have an explanation why some histograms are a better approximation to the
density than others? (Hint: you will need to scale the histogram appropriately so that the area
under the curve approximating the density is equal to 1.)
Correct syntax can be seen by using help rand and help hist.