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?
Last edited: Oct 29, 2013