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STAT 333 Test 2

# STAT 333 Test 2 - STAT 333 Winter 2010 Test 2 Thurs March...

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STAT 333 Winter 2010 Test 2 Thurs, March 18, 4:00 – 5:30 pm First (given) name:__________________ Last (family) name:____________________ Student ID #:__________________ UW userid:____________________ Instructions: 1. Please fill in the above information 2. This test has 7 pages, including this cover page 3. Answer all questions in the space provided 4. You have 90 minutes for the test 5. Show all your work and justify your steps 6. Good luck! Question Marks available Marks obtained 1 12 2 9 3 8 4 20 5 11 Total 60

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1. Suppose a monkey randomly and independently hits the white notes on a piano repeatedly, one at a time. The notes are {A, B, C, D, E, F, G}. [3] a) Find the expected # trials until the monkey first plays the melody “C D C D E D C D C”. [4] b) Derive the pgf F CDC (s) of the waiting time until the monkey first plays “C D C”. [3] c) Find the probability that “C D C” occurs for the first time on trial 6. (Hint: you can do this without expanding F CDC (s)) [2] d) What two things are required for a delayed renewal event to occur infinitely often?
2. A fair six-sided die is rolled repeatedly. Let λ be the event “the minimum roll so far is ≥ 3”

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STAT 333 Test 2 - STAT 333 Winter 2010 Test 2 Thurs March...

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