The results in Problem 1 were based on estimated probabilities. As such, whatever your determination in part (d) might be, it is at best an educated guess. In this problem, you will critically assess your answer in 1(d), by using simulations. Here, consider the case where, in fact, the events in 1(d) are independent. The advantage of making this assumption is that you can then generate the S-data independently of the R-data. Your investigation will use simulations. Use the truth model values: and . Because of our truth model, we know that . [Note: ]

(a)(10pts) Simulate measurements of the data collection variables . These will allow you to obtain estimates of the probabilities: , , and . Finally, you can use these to obtain estimates of the parameter . Note that because we know that S and R are independent, . Use your simulations to arrive at a simulation-based pdf for the estimator . [Hint: to arrive at perform a .* on the s & r data arrays.] [NOTE: You MUST include the command rng(shuffle) prior to these simulations.]

Solution: [See code @ 2(a).](PLEASE INCLUDE CODE)

Figure 2(a) Simulation-based pdf for .

(b)(5pts) Compute the value of associated your answers in 1(b)(i & ii) and 1(c). Then use Figure 2(a) to visually estimate the probability of the event that you would get an estimate greater than or equal to this value. [Show this event on your plot.]

Solution: [See red line in plot]

(c)(5pts) Use the Matlab command histcounts(ghat , [0 , 0.5 , 2 , max(ghat)]) to arrive at a numerical value for

.

Solution: