# Inferential statistics-maximum likelihood function

1. Aug 10, 2012

### kimkibun

1. The problem statement, all variables and given/known data

suppose that n cylindrical shafts are selected at random from the production of the machine and their diameters and lengths are measured. it is found that N11 have both measurements within the tolerance limits, N12 have satisfactory lengths but unsatisfactory diameters, N21 have satisfactory diameters but unsatisfactory lengths, and N22 are unsatisfactory to both measurements. ƩNij=n. each shaft may be regarded as a drawing from a multinomial population with density

p11x11p12x12p21x21(1-p11-p12-p21)x22; for xij=0,1; Ʃpij=1​

having three parameters. what are the maximum likelihood estimates of the parameter if N11=90, N12=6, N21=3, and N22=1?

2. Relevant equations

3. The attempt at a solution
my solution is attached. i just want to know if my answers are correct.

#### Attached Files:

• ###### 2.pdf
File size:
173.9 KB
Views:
74
Last edited: Aug 10, 2012