Exercise Set 12 Due Friday November 9th
Exercises 4.2 1,3,4,5
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Hint on 1 c) Think Binomial. Each atom can either survive longer
than time t (success) or not survive longer than time t
(failure). Nt = number of atoms out of 1024
surviving for at least t years is a binomial distribution with n = 1024,
and p = P(T>t) = ....... Want to find t such that E( Nt)
= 1.
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Hint on 1d) Approximate the Binomial distribution using the Poisson(np)
distribution.
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Hint on 4b) Median m says want P(W>m) = 1/2; solve for m.
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Hint on 4d) Let X = average of 100 independent and identically
distributed random variables so E(X) = _____ and Var(X) = ________ -- review
page 194. X is well approximated by the Normal distribution by the Central
Limit Theorem so now just plug and chug.
Hint on 4e) This is the Gamma Distribution with r = 2 --
P(W1 + W2 > 11) = P( Number of failures is less than 2), where number
of failures is Poisson with parameter _____.
Exercise Set 11: Due Wed November 14th
Exercises 4.5 1, 2, 3, 6, 8
Hints:
1. We will do part a in class -- just simple integration
2. These are step function since discrete -- see examples in
this section.
Sketch and also
write down what F(x) is at each point that it jumps
For part b)
note that the sum simplifies (see appendix page 516 bottom).
3 follows from
example 2 in text a) is just a simple observation of the symmetry.
b) Draw
the sketch, then calculate the probability as a proportion of the unit
6a), b), and c)direct
calculations from definitions.d) See page 316 -- X is the
maximum {Y1,
Y2, Y3}