3 - STAT 350 Fall 2008 Homework #3 Solution Corrected...

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STAT 350 – Fall 2008 Homework #3 – Solution Corrected through Lecture #6 Text Exercises Chapter 2, Problems #10, 14, 24 Chapter 5, Problem #2 2.10 () 1 b a fx EX x d x ba ⎛⎞ = ⎜⎟ ⎝⎠ ±²³²´ = 2 ab + 2.14 a. = 2 () () 2 22 0 0.5 x xd x = ±³´ b. for a continuous RV: ( )() () () () () () () 1 x x a b xf xd x a f x b x f x d x a f xd x b x x a f xd x b x x μ +∞ +∞ −∞ −∞ +∞ +∞ +∞ +∞ −∞ −∞ −∞ −∞ == += + ⎡⎤ ⎣⎦ =+ = + ∫∫ ±²³ ²´ ± ²³ ²´ OR for a discrete RV: ( ) ( ) ( ) 1 x x xpx a px b x px a b x a px b x + = + ∑∑ ±²³ ² ´± ²³ ²´ If the mean repair time is μ x = 0.5, the mean repair revenue is μ 25+40 x = 25 + 40 μ x = 45 Homework #3 – Solution Page 1 of 7
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2.24 a. () ( ) ( ) () ( ) N ( ) N ( ) N ( ) N ( N 2 22222 0.4 0.1 0.1 0.1 0.3 Var 1.8 01 . 8 0 11 . 8 1 21 . 8 2 31 . 8 3 41 . 8 4 Xx p x ppppp =− +− ) = 2.96 2.96 SD X = =1.72 b. P(1.8 - 1.72 < X < 1.8 + 1.72) = P(0.8 < X < 3.52) = p(1) + p(2) + p(3) = 0.1 + 0.1 + 0.1 = 0.3 P(X < 1.8 - 3 × 1.72 X > 1.8 + 3 × 1.72) = P(X < -3.36) + P(X > 6.96) = 0 5.2 A Venn diagram of these three events is a. b. Homework #3 – Solution Page 2 of 7
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c. d. e. Homework #3 – Solution Page 3 of 7
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f. Corrected: Then answer the following problems: 1. X is a continuous random variable with the following PDF. Find the mean of X . () 2 0.75 1 if 1 1 0o t h e r w i s e x x fx −− < = < 1 2 1 0.75 1 EX x x d x ⎡⎤ =− ⎣⎦ ±²²³ ² ²´ = 0 2. Using Minitab, create a Box-plot of the data you used in Lab #1.
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This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue University.

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3 - STAT 350 Fall 2008 Homework #3 Solution Corrected...

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