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Old 10-29-2018, 04:39 PM
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gauchodelpaso gauchodelpaso is offline
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Default Sample 242 - Range of possible solutions

This sample exercise is not excessively difficult or with lengthy calculations, unless your brain is tired like mine. If you are pressed for time, one method is to eliminate unlikely answers. In this case (being an old CAS there are ranges, but the comment is valid anyway):

(A) Less than 1.30
(B) At least 1.30, but less than 1.40
(C) At least 1.40, but less than 1.50
(D) At least 1.50, but less than 1.60
(E) At least 1.60

What I used was the range of possible q (0.2 to 0.5) and the Expected N conditional on q

E[N|q] = 0 * 0.1 + 1 *(0.9-q) + 2 * q = 0.9 + q (later used in the integration over q, multiplied by the posterior distribution)

Then the possible values of E[N] need to be between 1.1 and 1.4, pointing most likely to either (A) or (B). (C) is very borderline. And B is the right answer. I hope your coin flip is OK.

It pays at times to verify your solution to possible range of values. That if you have time. And we don't normally.
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