Question 3. Negative Binomial Distribution Suppose that in a group of insurance policies (which are independent as regards occurrence of claims), 45% of the policies have incurred claims (p=0.45). An auditor is examining the policies in the group one by one until 6 policies with claims are found (r=6). (a) Find the mean of X, E(X).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Question 3.
Negative Binomial Distribution
Suppose that in a group of insurance policies (which are independent as regards occurrence of
claims), 45% of the policies have incurred claims (p-0.45). An auditor is examining the policies
in the group one by one until 6 policies with claims are found (r-6).
(a) Find the mean of X, E(X).
(b) Find the variance of X, V(X), and the standard deviation, SD(X).
(c) Find P(X=7).
(d) Find P(X>11).
Transcribed Image Text:Question 3. Negative Binomial Distribution Suppose that in a group of insurance policies (which are independent as regards occurrence of claims), 45% of the policies have incurred claims (p-0.45). An auditor is examining the policies in the group one by one until 6 policies with claims are found (r-6). (a) Find the mean of X, E(X). (b) Find the variance of X, V(X), and the standard deviation, SD(X). (c) Find P(X=7). (d) Find P(X>11).
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