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?

the likely-hood estimator of p is = r / (r+x)

Step-by-step explanation:

Given:

- The succession of randomly selected mechanics until r = 18

- The total number of diagnostics by different mechanics n = 20

Find:

What is the mle of p?

Solution:

- Let X denote the number of incorrect diagnosis. The random variable X follows a negative binomial distribution with parameters r and p.

- The likely-hood function can be defined as:

- Apply natural logs on both sides of the likely hood function:

- Derivative with respect to p on both sides:

- Set the derivative to zero and we get:

- Thus, the likely-hood estimator of p is = r / (r+x)

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

the second option

step-by-step explanation: