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Exercise for November 22, 2008
May 1992 Course 110 Examination, Problem No. 35
Ten percent of all new businesses fail within the first year. The records of new
businesses are examined until a business that failed within the first year is found. Let X
be the total number of businesses examined prior to finding a business that failed within
the first year. What is the probability function for X?
A. 0.1⋅ 0.9 x , for x = 0,1, 2, 3,...
B. 0.9 ⋅ 0.1x , for x = 0,1, 2, 3,...
C. 0.1x ⋅ 0.9 x , for x = 1, 2, 3,...
D. 0.9x ⋅ 0.1x , for x = 1, 2, 3,...
E. 0.1⋅ ( x − 1) ⋅ 0.9 x , for x = 2, 3, 4,...
Solution.
Let a failure of a business be a success in a Bernoulli Trial, and a success of a business be
a failure in the same Bernoulli Trial. Then X has the geometric distribution with p = 0.1,
and therefore f X ( x ) = 0.1⋅ 0.9 x for x = 0, 1, 2, 3, … .
Answer A.
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