Homework Assignment 16:
(1) You are the agent for a baseball player who desires an incentive contract that will pay the following
amounts:
Type of hit
Probability of hit per time at bat
Compensation per hit
Single
0.14
x
Double
0.05
2
x
Triple
0.02
3
x
Home Run
0.03
4
x
The number of times at bat has a Poisson distribution with
λ
= 200.
The parameter,
x
, is determined
so that the probability of the player earning at least 4,000,000 is 0.95.
Using a normal approximation,
determine the player’s expected compensation. (Ans 5,532,122)
(2) The random variable, S, has a compound Poisson distribution with
λ
= 27/16 and claim amounts that
are uniformly distributed over [0,32].
The distribution is approximated by a translated gamma
distribution.
Show that the approximation for Pr(S>10) is given by
(3) A surplus process is given by U(t) = u + ct – S(t), t
≥
0.
For times t
≤
5, the history of claims is given
by the table below:
Claim Number
1
2
3
4
5
Time of Payment
0.5
1.25
2.75
3.50
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 Spring '11
 CharlesDann
 Poisson Distribution, Probability theory, Compound Poisson distribution

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