April 2012 CT3 Qn11(ii)

The exam paper is out on IOA website. Can anyone help to prove Question 11(ii)? It has been on my mind since the paper and really hates it when I can't prove it after so many tries during the exam and today as well.

Thanks in advance!!

 

question scan

 

Q11 Apr 2012

I think this was really a tough one and definitely worth more than the marks allotted.
To crack this, first compute the derivative of U(theta) wrt theta [as asked in part (i)].

To compute the expected value in part (ii), you need to note that

• 
  E(n_A) = n * theta

• 
  E(n_B) = n * theta * theta

• 
  E(n_C) = n * (1 - theta - theta * theta)

Plug in these in the equation and rest is algebra.

 

oh ya totally forgot about nA,nB,nC being variables

 

Could you please tell me what is the likelihood function here?

Is it - (theta)^n_a * (theta*theta)^n_b * (1 - theta - theta*theta0^n_c ?

 

Yes