st422%20hw02%20solution

st422%20hw02%20solution - Homework 2 Solutions 7.13 Y F(v1...

This preview shows pages 1–4. Sign up to view the full content.

Homework 2: Solutions 7.13: 2 1 2 2 1 22 12 21 (1 , 2 ) /1 /2 1/ ( 2, 1) v v vv YF v v v Y v UY F v v χ χχ = ⎛⎞ ⇒= = = ⎜⎟ ⎝⎠ 7.15: () 2 2 2 (1, ) / / v v v Z UT Fv v v 2 1 2 == = 5 2 1 2 5 2 2 i5 1 1 6 61 2 64 1 5 7.19: (0,1) 1,2. ..5 a) (thm 7.2) 4 b) U= Y (5 1) (thm 7.3) c) Given Y (0,1) Y Thus, S=U+Y i i i i Given Y N i WY YS N 2 5 = = + ∀= = −= = =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
64 6 16 5 6 26 4 22 6 66 7.20: From 7.19, Given Y (0,1), and U a) T = 5 / 5 b) T =2 / 4 c) (0,1/ 5) 5 and Y 2(5 +Y ) (5 +Y ) / 2 (2,4) /4 NW Y YW t W Y YU t U YN Y YY F UU χ χχ 2 2 5 11 = = ⇒= ∼∼ 7.22: 44 . 5 4 a) P( 4.5) 2/ 100 ( 2.5) 0.0062 b) Given =14 and =2 P(| | ) 0.95 | | 0.95 // || 0 . 9 5 / 1.96 / (1.96 2) / 100 0.392 Thus interval that in X XP PZ Xa P nn a n a n a μσ μ σσ σ ⎛⎞ −− >= > ⎜⎟ ⎝⎠ ⇒>= −< = ⇒< = = × = cludes ( ) (14 0.392) (13.608,14.392) =±= ± =
() 7.30: Given =10 and n=100 (1 1 ) ( | | 1 ) 11 || | | / / 10/ 100 | | 1 1 2 ( 1) 1 (2 0.1587) 0.6826 PY P Y Y PP Z nn PZ σ μμ μ σσ −<<+= −< ⎛⎞ =< = < ⎜⎟ ⎝⎠ = −> = × = 0.01/2 2 7.31: Given =10 P(| | 1) 0.99 (| | 1/( / )) (| | /10) /10 2.576 (25.76) 663.57 664 X n n nZ n −<= ⇒< ⇒= = = 7.34: Given =1.4, =0.05 and n=25 1.3 1.4 P( 1.3) 0.05/ 25 ( 10) 1 ( 10) 0 YP Z μσ ≤≈ =≤ = 100 1 7.42: Given =2.5, =2 and n=100 (2.5,4/100) (2.5,0.04) 2.4 2.5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

st422%20hw02%20solution - Homework 2 Solutions 7.13 Y F(v1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online