Mathematics, 26.02.2020 21:32, adazeb2003
A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 18 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 20 different mechanics (so there were 2 incorrect diagnoses). Let p = P(correct diagnosis), so p is the proportion of all mechanics who would correctly diagnose the problem. What is the mle of p?
Answers: 3
![f ( x; p , r ) = \left[\begin{array}{c}x+r-1&r-1\\\end{array}\right]*p^r*(1-p)^x](/tpl/images/0525/5012/45b8a.png)
![Ln |f ( x; p , r ) | = Ln |\left[\begin{array}{c}x+r-1&r-1\\\end{array}\right]| +r*Ln|p| + x*Ln|(1-p)|](/tpl/images/0525/5012/f3124.png)
![d (Ln |f ( x; p , r ) |)/dp = 0 +r/p - x/(1-p)\\\\Where , Ln |\left[\begin{array}{c}x+r-1&r-1\\\end{array}\right]| = Constant\\\\\\d (Ln |f ( x; p , r ) |)/dp = \frac{r - (r+x)*p}{p*(1-p)}](/tpl/images/0525/5012/aa4fa.png)
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A vehicle with a particular defect in its emission control system is taken to a succession of random...
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