8 Let X have the negative binomial distribution f(x) = (+=¦)p²(1-p)¹ for x=r,r+1,... (a) Obtain the maximum likelihood estimator of p. (b) For one engineering application, it is best to use components with a superior finish. Suppose X = 27 identical components are inspected, one at a time, before the r = 3rd component with superior finish is found. Find the maximum likelihood esti- mate of the probability that a component will have a superior finish.

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7.38 Let X have the negative binomial distribution
x-
f(x) =
(1) p²(1-P) X-P
p' (1-p) for x=r₁r+1, ...
(b)
(a) Obtain the maximum likelihood estimator of p.
For one engineering application, it is best to use
components with a superior finish. Suppose X =
27 identical components are inspected, one at a
time, before the r = 3rd component with superior
finish is found. Find the maximum likelihood esti-
mate of the probability that a component will have
a superior finish.
Transcribed Image Text:7.38 Let X have the negative binomial distribution x- f(x) = (1) p²(1-P) X-P p' (1-p) for x=r₁r+1, ... (b) (a) Obtain the maximum likelihood estimator of p. For one engineering application, it is best to use components with a superior finish. Suppose X = 27 identical components are inspected, one at a time, before the r = 3rd component with superior finish is found. Find the maximum likelihood esti- mate of the probability that a component will have a superior finish.
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