Problem 2 Now. let's consider the some problem in a different context. Suppose our samples are Unif(0. 9 = 1). We Proved in lecture that. 25' is unbiased for 0, but it should also be reasonably logical that the statistic 6 = maiden, ...,1:,.} is also unbiased for 9. Put another way - the parameter 0 is the maximum possible value, so if we simply use our maximum 06.3ch value, we should get a reasonable estimtor for 6. Using Monte Carlo. generate 10,011} samples of size n from Unif(0, 1) for n E {2. 5. 10. 20,50,100, 200, 300. 400.500}. Use apply() to your advantage. Compute 0 = max{:el,...,zn} for each sample. Plot how the average absolute percent error of 6 = changes with the sample size. Does it seem like the bias of this estimator changes with sample size? Problem 3 Repmt Problem 2. but use 5 - 25' instead. Does it noun like the bias of this (minister changes with sample size? (Remember - we proved this estimator is unbiased. regardless of n!) Using Monte Carlo, generate 10,000 samples of size n from N( = 100, a = 5) for n E {2, 5, 10, 20, 50, 100, 200, 300, 400, 500}. Use lapply () to your advantage. Compute s' for each sample. Plot how the absolute percent error of s', changes with the sample size. Comment on the bias of s'. sampler