1 . Let (21, 22, . .. ,28) be i.i.d. samples of a random variable X with mean and variance o'. Consider the following estimators of /: M1 = 12 = : 201 - 25 + 23 2 (a) Is either estimator unbiased? (b) Which of these two estimators is better? In what sense is it better? 2. Out of 1000 randomly selected patients diagnosed with lung cancer, 834 died within 10 years. (a) Construct a 95% two-sided confidence interval on the 10-year death rate from lung cancer. (b) How large a sample would be required to be at least 95% confident that the margin of error in estimating the 10-year death rate from lung cancer is less than 0.02? 3. Let (x1, 22, . .. , In) be i.i.d. samples from a random variable X with the following probability density function: fx(x) = 0x-1, 0 0, find the maximum a posteriori estimate of 0. Note that the probability density function of an exponential random variable is given by: TT (0) = boe-Bob, 0 >0