05 STAT HWB a - Dr. V.R. Bencivenga Economics 329 PRACTICE...

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Dr. V.R. Bencivenga Economics 329 PRACTICE HOMEWORK #5B: RIGHT ANSWERS 1.a. 36 . 36 . 28 . 1 ) 1 X ( P ) 0 X ( P 1 ) 1 X ( P b. 87 . 04 . 09 . 1 ) 4 X ( P ) 3 X ( P 1 ) 3 X ( P c. Define X i = number of times car i will need to be returned, i = 1,…, 10 P(any one car will not need to be returned during the warranty period) = 28 . ) 0 X ( P i 000003 . 28 . ) 0 X ( P ... ) 0 X ( P ) 0 X ( P ) 0 X ... 0 X 0 X ( P 10 10 2 1 10 2 1 Note that we are assuming that the ten cars in the fleet are statistically independent. d. 25 . 1 ) 04 (. 4 ) 09 (. 3 ) 23 (. 2 ) 36 (. 1 ) 28 (. 0 ] X [ E 1675 . 1 3025 . 275625 . 129375 . 0225 . 4375 . ) 04 (. ) 25 . 1 4 ( ) 09 (. ) 25 . 1 3 ( ) 23 (. ) 25 . 1 2 ( ) 36 (. ) 25 . 1 1 ( ) 28 (. ) 25 . 1 0 ( ) X ( Var 2 2 2 2 2 e. Use the mean and variance of a linear transformation. 75 . 968 , 72 ) 1675 . 1 ( 250 ) X ( Var 250 ) X 250 100 ( Var 5 . 412 ) 25 . 1 ( 250 100 ] X [ E 250 100 ] X 250 100 [ E 2 2 2. Obviously, there are many possible examples. The simplest type of example is one with some zero probabilities, and “symmetry” in the distribution of X and Y. X 1 2 3 1 .2 0 .2 Y 2 0 .2 0 3 .2 0 .2 3.a. Use the marginal probabilities of X to compute the mean and variance of X. 000 , 10 ) 3 (. 000 , 15 ) 4 (. 000 , 10 ) 3 (. 5000 ] X [ E b. 000 , 000 , 15 ) 3 (. ) 000 , 10 000 , 15 ( ) 4 (. ) 000 , 10 000 , 10 ( ) 3 (. ) 000 , 10 5000 ( ) X ( Var 2 2 2 c. Repeat the previous two parts, using the conditional probabilities of X given Y = 7,000. 67 . 6666 3 . 0 000 , 15 3 . 1 . 000 , 10 3 . 2 . 5000 ] 7000 Y | X [ E         56 . 555 , 555 , 5 296 . 696 , 703 , 3 259 . 859 , 851 , 1 3 . 0 67 . 6666 000 , 15 3 . 1 . 67 . 6666 000 , 10 3 . 2 . 67 . 6666 5000 7000 Y | X Var 2 2 2
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2 d. In the following expression for the covariance, all nine terms are listed, although only the third and seventh are non-zero.                                       000 , 000 , 4 000 , 000 , 2 000 , 000 , 2 0 5000 7000 000 , 10 000 , 15 1 . 5000 7000 000 , 10 000 , 10 2 . 5000 7000 000 , 10 5000 1 . 5000 5000
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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 at Austin.

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05 STAT HWB a - Dr. V.R. Bencivenga Economics 329 PRACTICE...

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