Mathematics 210  Spring term 2005  Seventh assignment
This assignment requires you to submit spreadsheets concerned
with discrete probability distributions.
It is due before class time Monday, March 14.

Go to the MathSheet home page
and then to the new applet page. Open a running
copy of the spreadsheet and return to this page.

Log in immediately: File/Log in. Your login id is your
Mathematics Department login name, and your password
is your student number. This allows you to save
and load spreadsheet files.
Save your work frequently.
To put it in simpler terms,
save your work frequently.

Question 1.
Place the probability p = 1/2 in a0 and the integers N=8 in
a1. In column b place the numbers
0 to 256. In column c place the probabilities of getting
k heads in a toss of N loaded coins for which the probability of getting a single head is p. Be sure that a chnage in p
will still produce the correct distribution.
Make a bar graph of the probabilities.
Save as m210.7.1.ms.

Question 2.
Place in columns d on the same probabilities for N=16,
32, ..., 256. Graph them all on one plot,
the larger values of N on top of the earlier ones.
Place a line plot through the maximum points of each.
Comment on the ratio of successive maxima  the sequence of maximum
probabilities of the distributions.
Also, put somewhere clearly the means and standard deviations of
each of these distributions.
Save as m210.7.2.ms.

Question 3.
Exactly the same as the previous question,
except now change p to 1/32.
Several of you have been having trouble here
with spreadsheets freezing up.
If this happens to you, it's probably
because you are attempting to calculate
numbers smaller than the computer can
handle. How can you get around this?
Save as m210.7.3.ms.

Question 4.
Set up a spread sheet so the values 1 to 64 are in column a,
in column b the probabilities 1/6 in rows 0 through 7.
In column c place the probabilities of the sums of two values,
and in column d the sums of three, in e
taht of four. (That is to say, these
record the probabilities of getting various sums from the top of tossed dice.)
Graph these, the last on top of the first.
Also, put somewhere clearly the means and standard deviations of
each of these distributions.
Save as m210.7.4.ms.
If you find these questions confusing, please
write me.
