Calculus for Biologists Lab
Math 1180-002
Spring 2012
Assignment #6 - Discrete Random Variables
Report due date: Tuesday, February 28, 2012 at 9 a.m.
? Please number your responses to each problem in your write-up.
1. List the new R commands you used in the lab and describe, in general, what they do. Use your own words,
not mine!
2. (a) Include Plot 6.1 from lab 6. Describe in detail the similarities and differences you see between the two
histograms, and explain any differences you observe.
(b)
i. What was the true expected value you calculated for the number of purple offspring?
ii. How do you interpret this number biologically?
iii. What is the estimated expectation of the number of purple offspring you computed from your
simulation results?
iv. How does the estimated expectation compare to the true one?
3. (a) Include Plot 6.2 from lab 6. Which sum was obtained the greatest number of times, based on this
histogram?
(b) Which sum was obtained the fewest number of times?
(c) List all of the possible sums that can be obtained by rolling two dice.
(d) Write the entries of the table est.prob.sums. Be sure to include the column headers.
(e) How many rolls of the dice (out of 100) resulted in a sum of 5?
(f) Calculate the actual probabilities (using math, not R) of obtaining each of the possible sums on a
given roll of the dice.
(g) Use the results in 3d and 3f to calculate the the estimated and true expected values for these sums.
(h) How does your estimate compare to the actual expectation?
(i) How does your histogram reflect the estimated expectation?
? Save your report as a .pdf file and upload it to Blackboard.
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