## 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.
• 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.

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• 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.