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Exercise 2.69

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(a)

y = dp + (1 - d) (1 - p)

(b)

The worst choice for

p

\frac{1}{2}

, because then the fraction of "yes" responses is

\frac{1}{2}

irrespective of the fraction of drug users. In other words, the number of "yes" responses tells us nothing.

(c)

We can extend the result from part

a

A drug user says "yes" either if they get a "Have you used drugs" slip, or if they get a "I was born in winter" slip and they are, in fact, born in winter.

A person who has not used drugs says "yes" only in the case that they get a "I was born in winter" slip and they were, in fact, born in winter.

y = d (p + \frac{1}{4} (1 - p)) + (1 - d) (1 - p) \frac{1}{4}

Thus,

d = \frac{4 y + p - 1}{2 p}

fifthist

2021-12-05 00:00

Exercise 2.69

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