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econ483quiz01sol

# econ483quiz01sol - (True or False& is a random variable...

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Your Name: Let f X i g be a sequence of independent and identically distributed ( iid ) random variables, with some distribution where E [ X i ] = and V ar ( X i ) = ± 2 for i = 1 ; :::; n . Also, let Y be another random variable. 1. (True or False) E [ X i ] is a random variable. Explain. (1-2 sentences.) False, because randomness in X i is integrated (or summed) out. 2. (True or False) E [ X i j Y ] is a random variable. Explain (1-2 sentences.) True, because E [ X i j Y ] is a function of Y . 3. The Law of Large Numbers (LLN): 1 n n P i =1 X i ! p , as n ! 1 (True or False) 1 n n P i =1 X i is a random variable. Explain (1-2 sentences.) True, because sum of random variables is a random variable.
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Unformatted text preview: (True or False) & is a random variable. Explain (1-2 sentences.) False, because & is a nonrandom constant. 4. The Central Limit Theorem (CLT): 1 p n n P i =1 ( X i & & ) ! d N & ; ± 2 ± , as n ! 1 (True or False) 1 p n n P i =1 ( X i & & ) follows a normal distribution. Explain (1-2 sentences.) False, because distribution of X i is unknown. (True or False) N & ; ± 2 ± follows a normal distribution. Explain (1-2 sentences.) True, by de±nition. 1...
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