Question : It is assumed that the arrival of number of calls per hour follows Poisson distribution with parameter . A random sample is taken. Obtain the maximum likelihood estimate of the average arrival rate
Yes, but I realise now that I misread the question - this distribution is not relevant (which is not to say that it's not relevant to you in the broader context of developing and consolidating your general understanding).
Here is a Christmas present:
The likelihood function is .
Therefore .
Your job is to solve for . The answer is not surprising.