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Assign7 - 01 4 Pr 2 2 2 1 = S S Problem 6.40 a What happens...

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STA 3032 – Assignment 7 Problem 5.72: Two independent binomial random variables with 2 = n and 3 . 0 = p . a.) Joint distribution: 2 1 2 1 2 2 1 1 4 2 1 2 2 2 1 2 1 ) 7 . 0 ( ) 3 . 0 ( 2 2 ) 7 . 0 ( ) 3 . 0 ( 2 ) 7 . 0 ( ) 3 . 0 ( 2 ) , ( x x x x x x x x x x x x x x f - - + - - = × = Or in tabular format: 0 1 = X 1 1 = X 2 1 = X 0 2 = X 0.2401 0.2058 0.0441 1 2 = X 0.2058 0.1764 0.0378 2 2 = X 0.0441 0.0378 0.0081 b.) ) Pr( 2 1 X X < : 2877 . 0 0378 . 0 0441 . 0 2058 . 0 ) 7 . 0 ( ) 3 . 0 )( 1 )( 2 ( ) 7 . 0 ( ) 3 . 0 )( 1 )( 1 ( ) 7 . 0 ( ) 3 . 0 )( 2 )( 1 ( ) 2 , 1 ( ) 2 , 0 ( ) 1 , 0 ( ) Pr( 1 3 2 2 3 1 2 1 = + + = + + = + + = < f f f X X Problem 5.124: 127 ) 4 ( 25 ) 3 ( 9 ) ( Var 25 ) ( Var 9 ) 2 5 3 ( Var 8 2 ) 1 ( 5 ) 5 ( 3 2 ) ( E 5 ) ( E 3 ) 2 5 3 ( E 2 1 2 1 2 1 2 1 = + = + = + + - = + + - = + + = + + X X X X X X X X Problem 6.34: a.) Chebyshev’s Theorem: ( 29 ( 29 08 . 0 ) 4 . 0 ( 5 . 0 75 . 3 5 . 1 2 1 75 . 3 63 Pr 2 1 75 . 3 63 Pr 5 . 1 36 / 9 2 2 = = = - = - = = X X X σ
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b.) Central Limit Theorem: 0062 . 0 9938 . 0 1 ) 5 . 2 Pr( 1 5 . 2 5 . 1 63 Pr ) 75 . 66 Pr( = - = < - = - = Z X X Problem 6.36: ( 29 ( 29 9876 . 0 0062 . 0 9938 . 0 5 . 2 Pr 008 . 0 02 . 0 25 / 04 . 0 Pr 02 . 0 Pr = - = = - = - Z X X μ μ Problem 6.38: Find ) 4 / Pr( 2 2 2 1 S S . In this case, 2 2 2 1 / S S has an F distribution with 8 1 = ν and 15 2 = ν degrees of freedom. From Table 6(b), we find that
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Unformatted text preview: 01 . ) 4 / Pr( 2 2 2 1 = S S . Problem 6.40: a.) What happens to the standard error when the sample size is increased from 100 to 200? 7071 . 5 . 200 100 100 / 200 / 100 200 = = = = σ b.) What happens to the standard error when the sample size is increased from 200 to 300? 8165 . 6 66 . 300 200 200 / 300 / 200 300 = = = = c.) What happens to the standard error when the sample size is decreased from 360 to 90? 2 4 90 360 360 / 90 / 360 90 = = = =...
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