Homework Assignment 17:
(1)
For an allosaur with 10,000 calories stored at the start of a day:
(i)
The allosaur uses calories uniformly at a rate of 5,000 per day.
If his stored calories reach 0,
he dies.
(ii)
Each day the allosaur eats 1 actuary (10,000 calories) with probability 0.45 and
no actuary with probability 0.55.
(iii)
The allosaur eats only actuaries.
(iv)
The allosaur can store calories without limit until needed.
Find the matrix
A
in Theorem 1 of the handout, and use it to determine the probability that the allosaur
ever has 15,000 or more calories stored. (Ans 0.598)
(
An online matrix calculator is available at http://wims.unice.fr/wims/wims.cgi)
(2) A coinflipping games requires the player to repeatedly flip an unbiased coin until the
difference
between the number of heads tossed and the number of tails tossed is
three.
Find the matrix
N
in Theorem 2 of the handout, and use it to determine the expected number of flips
before the game ends. (Ans 9)
(3)
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 Spring '11
 CharlesDann
 Probability theory, Markov chain, insurance company, probability matrices Qn

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