1. consider a large population which has population mean µ, and population variance σ2. we take a sample of size n = 3 from this population, thinking of the samples as realizations of the rvs x1, x2, and x3, where the xi can be considered iid. we are interested in estimating µ. (a) consider the estimator ˆµ1 = x1 + x2− x3. is this estimator unbiased for µ? explain your answer.

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?