05 STAT HWA a

# 05 STAT HWA a - Dr Valerie R Bencivenga Economics 329...

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1 Dr. Valerie R. Bencivenga Economics 329 PRACTICE HOMEWORK #5A: RIGHT ANSWERS 1.a. 9 . 1 ) 1 (. 4 ) 2 (. 3 ) 3 (. 2 ) 3 (. 1 ) 1 (. 0 ] X [ E 29 . 1 ) 1 (. ) 9 . 1 4 ( ) 2 (. ) 9 . 1 3 ( ) 3 (. ) 9 . 1 2 ( ) 3 (. ) 9 . 1 1 ( ) 1 (. ) 9 . 1 0 ( ] X [ Var 2 2 2 2 2 b. Daily income X 20 30 Y 516 ] X [ Var 20 ] Y [ Var 68 ] X [ E 20 30 ] Y [ E 2 c. Let X i , i =1,2 be the number of bikes sold on day i X i are iid with E[X] = 1.9 and Var[X] = 1.29 Total income = T = 30 + 20X 1 + 30 + 20X 2 = 60 + 20X 1 + 20X 2 1032 ] X [ Var 20 ] X [ Var 20 ] T [ Var 136 ] X [ E 20 ] X [ E 20 60 ] T [ E 2 2 1 2 2 1 There is no covariance term because X 1 and X 2 are independent d. Average income = A = T 2 1 = 30 + 10X 1 + 10X 2 258 ] X [ Var 10 ] X [ Var 10 ] A [ Var and , 68 ] X [ E 10 ] X [ E 10 30 ] A [ E 2 2 1 2 2 1 Alternatively,     68 136 2 1 T E 2 1 A E , and       258 1032 4 1 T Var 2 1 A Var 2 Note Var[A] < Var[Y] 2.a. This is a probability function each probability is non-negative, and the probabilities sum to 1 : 1 10 4 10 3 10 2 10 1 x 10 1 4 , 3 , 2 , 1 x , 0 x 10 1 4 1 i i i i b. For the same reasons, this is also a probability function: 10 1 i i 1 10 1 10 ..., , 3 , 2 , 1 x , 0 10 1 c. This is not a probability function. Each probability is non-negative. However, the probabilities do not sum to one: ... 2 . 2 . 2 . 2 . 3 2 1 i x i This is a geometric sum except for the first term (the “1”): 25 . 1 2 . 1 1 ... 2 . 2 . 2 . 1 3 2 . Therefore, the probabilities sum to 25 . 1 25 . 1 .

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2 3.a. i x i j x X where e   i X x P 0 8 e .063 1 7 6 5 e , e , e .321 2 4 3 2 e , e , e .469 3 1 e .147 b. Not all sequences with 2 hits win the game (the 2 hits have to be sequential, so the sequence in 4 e does not win the game). Accordingly,   ) win ( P 273 . 147 . 469 . 2 X P c. No. Although X gives the number of “successes” (hits) in 3 trials, and the trials are independent, they are not identically distributed (the probability of a hit is different when she bats R and L). 4.a. P(X = 2 Y = 1) = .05 b. E[Y] = 1(.25) + 2(.35) + 3(.4) = 2.15 Var(Y) = (1 2.15) 2 (.25) + (2 2.15) 2 (.35) + (3 2.15) 2 (.4) = .6275 c.       167 .
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## This note was uploaded on 02/26/2012 for the course ECONOMICS 329 taught by Professor Bencivenga during the Spring '12 term at University of Texas.

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05 STAT HWA a - Dr Valerie R Bencivenga Economics 329...

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