Consider three types of claims: A, B and C. Let XẠ denote the rand variable for the size of a randomly chosen claim of type A, and let and Xc denote the corresponding random variables for claims of ty B and C, respectively. Assume that XA, XB and Xc are exponentially distributed with parar ters A = 0.002, XB = 0.001 and Xc = 0.005, respectively.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Probability.

Consider three types of claims: A, B and C. Let XẠ denote the random
variable for the size of a randomly chosen claim of type A, and let XB
and Xc denote the corresponding random variables for claims of types
B and C, respectively.
Assume that XA, XB and Xc are exponentially distributed with parame-
ters lA = 0.002, \B = 0.001 and Ac = 0.005, respectively.
An insurance company has a portfolio of policies with 10% of claims of
type A, 20% of type B, and the remaining claims of type C.
Let X denote the random variable for the size of a claim chosen at ran-
dom from all those on policies in the portfolio.
(a) Calculate Pr(X > 100), the probability that a randomly chosen claim
is greater than 100.
Transcribed Image Text:Consider three types of claims: A, B and C. Let XẠ denote the random variable for the size of a randomly chosen claim of type A, and let XB and Xc denote the corresponding random variables for claims of types B and C, respectively. Assume that XA, XB and Xc are exponentially distributed with parame- ters lA = 0.002, \B = 0.001 and Ac = 0.005, respectively. An insurance company has a portfolio of policies with 10% of claims of type A, 20% of type B, and the remaining claims of type C. Let X denote the random variable for the size of a claim chosen at ran- dom from all those on policies in the portfolio. (a) Calculate Pr(X > 100), the probability that a randomly chosen claim is greater than 100.
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