SAMPLE FIRST MIDTERM WITH SOLUTIONS
AMS 550
SPRING 2010
1. Two coins are tossed simultaneously and repeatedly. Coin i has a probability pi of showing
i
a head, 0 < pi < 1, i = 1, 2, Let Sn be the numb
SAMPLE FIRST MIDTERM, AMS550
1. Two coins are tossed simultaneously and repeatedly. Coin i has a probability pi of showing
i
a head, 0 < pi < 1, i = 1, 2, Let Sn be the number of heads observed during
SAMPLE SECOND MIDTERM SOLUTIONS, AMS550, SPRING 2013
1. Buses and cars arrive to an intersection according to independent Poisson processes with
intensities and respectively. At time 0 the intersectio
SECOND MIDTERM SOLUTIONS, AMS550
1. Let X be Bobs remaining lifetime without a Kidney and let Y be the time of availability of the Kidney. Then X and Y are independent, X exp(), and Y exp(). We have
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Homework 2 Solution
4.18 If the state at time n is the nth coin to be flipped then sequence of consecutive states
constitute a two state Markov chain with transition probabilities:
P ,1 = .6 = 1 P , P
Homework 1 (due 2/7)
1. Read sections 4.14.3 for the covered material and 4.44.7 for the future material.
2. Writing assignment:
Problems 3, 5, 6, 8, 13, 14, 15 from Chapter 4 (starting on page 275)
Homework 2 (due 2/14)
Read Sections 4.44.5 of the text.
Problems 18, 20, 22, 25, 31, 33 from Chapter 4.
Remarks:
Most of the problems are on the material of Section 4.4.
Proportion of time that an ir
Homework 3 (due 2/21)
Read Problem 13 on p. 481 (Walds equation, Chapter 7) and read Sections 4.6 and 4.7 of
the text.
Writing assignment:
Problems 15 and 16 from Chapter 7 and 34, 45, 52 from Chapter
Homework 4 Solution
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