Suppose we want to maximize this likelihood with respect to:

L(|y1,...yn)=ni=11eyi/L(|y1,...yn)=i=1n1eyi/

1. What is an expression for the log-likelihood of given our datay1,...yny1,...yn? Include this in your Rmd document.
2. Differentiate the log-likelihood with respect to and write down the equation that our MLE satisfies.
3. What is the analytic solution to this equation?
4. Derive the updating equation forii that is used by Newton's algorithm.
5. Run Newton's algorithm withn=10n=10 observations, from the starting point0=20=2 when
   1. 1. y=10y=10
      2. y=25y=25
      3. y=0.5y=0.5

Are there any problems in finding a maximum in these cases? (Note: Creating a function for Newton's Algorithm will be very helpful).