3. The "Sample Variance" Let be i.i.d. (discrete or continuous), each with mean and SD . Let be the sample mean. (a) Find and . It's fine to just quote answers derived in class or in the textbook. (b) For each , find . [Plug in the definition of and use bilinearity.] (c) For each in the range 1 through , define the th deviation in the sample as . Find and . [Write the variance as , plug in the definition of , and use bilinearity.] (d) Define the random variable as Find . For this random variable, the notation is pretty standard in statistics. Just think of as a symbol; it doesn't help to start thinking about the random variable that is its square root. (e) Use Part d to construct a random variable denoted that is an unbiased estimator of . This random variable is called the sample variance and is frequently used in inference