320_hw4_ans

320_hw4_ans - Economics 320 Homework 4 Answers 1. Find the...

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Economics 320 Homework 4 Answers 1. Find the Probability that X = 2 for each of the following: a. P(x) = (1/33)x 5 x=1,2 b. P(x) = (1/1312)(x 5 +3) x=1,2,3,4 a. P(2) = (1/33)(2 5 ) = 32/33 = 0.9697 b. P(2) = (1/1312)(2 5 + 3) = 0.0267 2. For each of the following probability functions find the mean and the variance of the random variable. a. P(x) = (1/33)x 5 x=1,2 b. P(x) = (1/1312)(x 5 +3) x=1,2,3,4 c. P(x) =( 1/266)(x 2 +x 3 ) x=3,4,5 a. P(x) = (1/33)x 5 x=1,2 = = = = x x x x x x x xP x E 6 5 ) 33 / 1 ( ) 33 / 1 )( ( ) ( ) ( (1/33) + (64/33) = 65/33 = 1.97 2 2 2 2 ) ( ) ( μ ο - = - = x E x E . We already have μ so all we need is E(x 2 ). = = = = x x x x x x x P x x E 7 5 2 2 2 ) 33 / 1 ( ) 33 / 1 )( ( ) ( ) ( (1/33) + (128/33) = 129/33 = 3.91 σ 2 =3.91-(1.97) 2 = .03 b. P(x) = (1/1312)(x 5 +3) x=1,2,3,4 + = + = x x x x x x E 3 1312 / 1 ) 3 )( 1312 / 1 )( ( ) ( 6 5 =1/1312[(1+3)+(64+6)+(729+9)+(4096+12)] =3.75 + = + = x x x x x x E 2 7 5 2 2
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320_hw4_ans - Economics 320 Homework 4 Answers 1. Find the...

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