hmm..so in this case i should use the multinomial prob. mass function to get the likelihood function.. then take the natural log of it correct?
Do I differentiate now and how do I arrive at the estimate for theta?
i'm a little lost at this point, in the above section it says that for example green marbles is modeled by a r.v. N1 with a binomial (n, 1/4(θ+2)) distribution and blue is modeled by r.v. N2 with a binomial (n,1/4(θ)) dist. where n in both cases is total # of marbles (3839 in this case)
so I'm...
oops i left out that x=1,2,3,4 are of binomial distributions...
would the likelihood function be the pmf of binomial dist.?
= (nCx) p^x (1-p)^(n-x)
and the loglikelihood function be:
L(p)= log(nCx) + xlog(p) + (n-x)log(1-p) ??
in need of help for how to do this question
given probability mass function:
x 1 2 3 4
p(x) 1/4(θ+2) 1/4(θ) 1/4(1-θ) 1/4(1-θ)
Marbles
1=green
2=blue
3=red
4=white
For 3839 randomly picked marbles
green=1997
blue=32
red=906...