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Q&A Bank 3.21 (ii)

Nolasko said:
Can someone please explain me how the MLE is derived here, particularly the constant part?
Click to expand...

The probability of observing 87,889 zero's is \([P(X=0)]^{87.889}\), the probability of observing 11,000 one's is \([P(X=1)]^{11,000}\) and so on. You then use the probability function for the Poisson to get \(P(X=0)\), etc.

The constant is all the different combinations of getting 87,889 zero's, 11,000 one's and so on. Just like a binomial. But frankly it doesn't affect your answer so I wouldn't bother with the actually value and just call it constant.
 
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