(Solved): 3. [25 points] Suppose that {X} is a random sample from some unknown distribution (denoted by f(x, ...

3. [25 points] Suppose that {X} is a random sample from some unknown distribution (denoted by f(x,0*)) with unknown mean u and known variance of =1. We are interested in estimating u* by using the sample mean (denoted by û). In statistics, sampling error is the error caused by observing a sample instead of the whole population. In our context, the sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter. (i) Explain what measure you can use to calculate the sampling error in our case. (ii) Suppose that you wish to make P(| ?* - | > 0.1) smaller than 1%. How many observations at least do you need to have?