Homework 3.pdf - Econ41(SummerC2017 ,UCLA Instructor:MingGu...

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Econ 41 (Summer C 2017)  Department of Economics, UCLA  Instructor: Ming Gu  Homework 3  Due: Wed 9/6 before lecture  1. Suppose that  ܺ , ܺ , … , ܺ  are independent and identically distributed random variables with the  common mean  and variance  . Calculate   (a) the mean of  Y ൌ ሺܺ െ ߤሻ ௜ୀଵ    (b) the variance of Y   (c) the mean of  Z ൌ ୬ିଵ ሺܺ െ ܺ ௜ୀଵ , where  ܺ  is the sample mean.     2. Suppose that X is a random variable with pdf  fሺxሻ ൌ ݁ ି  , 0   x <    Compute (a) E(X) (hint: use integration by parts)  (b) P (X > 9| X > 6). Show that it is equal to P (X > 3).    3. Suppose that  ܺ , ܺ , … , ܺ  are a random sample from N ( ,  1). Let  ܺ  be the sample mean. What is the  distribution of (a)  ܺ
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