Simulate a random sample of size n = 100 from the zero-truncated distribution when  = 2. [Note that you can do this by simulating data from the (un-truncated) Poisson distribution and discarding the zeros.] i. Provide R code which returns the value of the log-likelihood for a given data vector, x, and parameter value, . ii. Provide R code which returns the maximum likelihood estimate of  for a given data vector. iii. Provide a single plot which shows:  ---the log-likelihood in the range 1<=lambda<= 5, if we assume the data comes from the Poisson distribution;  ---the log-likelihood in the range 1<=lambda<= 5, if we assume the data comes from the zero-truncated Poisson distribution;  ---the maximum likelihood estimate for  for both the Poisson distribution and the zero-truncated Poisson distribution. iv. Derive an expression for the dierence between the two log-likelihood functions, and hence comment on your plot in (iii). Comment on how well each of the MLEs estimates the true value of  Thank you for everybody, Regards,