IAI - May 2012

I couldn't understand the solution to part (b) of Q.7. The main problem I faced was in the portion before the likelihood function was calculated.

 

Debjit

Can you point out the step which is not clear?

 

These steps:



[Image link: http://postimg.org/image/gjmiwtn07/]

 

Debjit

In this scenario you are told that you do not know X1, X2 ... but only whether Xi = 0 or Xi > 0.

Step 1: You define the new random variables Y1, Y2 , .... These Yi-s can take one of only two values 0 or 1

Since the likelihood will be based on probabilities of Yi-s,

Step 2: Compute P(Yi = 0) and P(Yi = 1). Note the sum of the two probabilities has to be 1.

Step 3: Set up the likelihood function.

If you are confused with how the likelihood function is written, you can check one of two things:

a. For each factor within the likelihood function, plug in and observe what happens if you have Yi = 0 or Yi =1. Do you get the correct probabilities?

b. Revise the section on how to write the likelihood function if the distribution of the underlying random variables is Bernoulli with probability of success p = 1 - exp(-lambda).

Does this help?

 

I get it now! I just couldn't recall the poisson-binomial approximation. Thanks a lot! :

 

You are welcome !

Not sure I got the last part of your comment 'Poisson-Binomial approximation' ... this question has nothing to do with that !

 

Sorry! Misprint! I meant Poisson-Bernoulli.

 

Again this question has nothing to do with Poisson-Bernoulli approximation.

I suggest that you re-read the question and solution.