(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

suppose thatncylindrical shafts are selected at random from the production of the machine and their diameters and lengths are measured. it is found that N_{11}have both measurements within the tolerance limits, N_{12}have satisfactory lengths but unsatisfactory diameters, N_{21}have satisfactory diameters but unsatisfactory lengths, and N_{22}are unsatisfactory to both measurements. ƩN_{ij}=n. each shaft may be regarded as a drawing from a multinomial population with density

p_{11}^{x11}p_{12}^{x12}p_{21}^{x21}(1-p_{11}-p_{12}-p_{21})^{x22}; for x_{ij}=0,1; Ʃp_{ij}=1

having three parameters. what are the maximum likelihood estimates of the parameter if N_{11}=90, N_{12}=6, N_{21}=3, and N_{22}=1?

2. Relevant equations

3. The attempt at a solution

my solution is attached. i just want to know if my answers are correct.

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# Homework Help: Inferential statistics-maximum likelihood function

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