Question
Let X=+W , where and W are independent normal random variables and W has mean zero. a) Assume that W has positive variance. Are X
LetX=+W , whereandWare independent normal random variables andWhas mean zero.
a) Assume thatWhas positive variance. AreXandWindependent?
b) Find the MAP estimator ofbased onXifN(1,1)andWN(0,1), and evaluate the corresponding estimate ifX=2, then theta-hat = jQuery224007732290526419172_1541075699061??
c) Find the MAP estimator ofbased onXifN(0,1)andWN(0,4), and evaluate the corresponding estimate ifX=2, then theta-hat = ????
d) For this part of the problem, suppose instead thatX=2+3W, whereandWare standard normal random variables. Find the MAP estimator ofbased onXunder this model and evaluate the corresponding estimate ifX=2, then theta-hat = ????
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Elementary Statistics
Authors: Mario F. Triola
11th Edition
321500245, 321500243, 978-0321500243
