Hw3_2700_s09

# Hw3_2700_s09 - ENGRD2700 Basic Engineering Probability and...

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ENGRD2700 Basic Engineering Probability and Statistics Spring 2009 Homework 3: Conditional Probability, Independence, Discrete Random Variables. Hand in by 1:30 pm on Friday, February 13 in the ENGRD2700 dropbox. Be sure to write your name and section number (1–6) on your homework. Make sure that your homework pages are stapled together. This homework has 10 parts. NOTE: Your answers will, as always, be graded on the clarity of your writing as well as the correctness of the answer. You must show your work to receive full credit. 1. Disjointness and Independence Roll two dice and let A = ”the first die is 4”. Let B 1 = ”the second die is 2”. Assume equal likelihood for each of the six sides on each die. Intuitively the outcome of the first has nothing to do with the outcome of the second. (a) Check whether the events A and B 1 are independent. (b) Let B 2 = ”the sum of the two dice is 3”. Are the events A and B 2 disjoint? Why? (c) Are the events A and B 2 independent? Why? (d) Let B 3 = ”the sum of the two dice is 9”. Are the events A and B 3 disjoint? Why? (e) Are the events A and B 3 independent? Why? (f) Let B 4 = ”the sum of the two dice is 7”. Are the events A and B 4 disjoint? Why? (g) Are the events A and B 4 independent? Why? (h) Briefly state some conclusions you have drawn from this question.

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