{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mont4e_sm_ch05_sec05

# mont4e_sm_ch05_sec05 - 5-54 a E(2X 3Y = 2(0 3(10 = 30 b...

This preview shows pages 1–2. Sign up to view the full content.

5-37 5-54 a) E(2X + 3Y) = 2(0) + 3(10) = 30 b) V(2X + 3Y) = 4V(X) + 9V(Y) = 97 c) 2X + 3Y is normally distributed with mean 30 and variance 97. Therefore, 5 . 0 ) 0 ( ) ( ) 30 3 2 ( 97 30 30 = < = < = < + Z P Z P Y X P d) 8461 . 0 ) 02 . 1 ( ) ( ) 40 3 2 ( 97 30 40 = < = < = < + Z P Z P Y X P 5-55 (a) E(3X+2Y)= 3*2+2*6=18 (b) V(3X+2Y) = 9*5+4*8 =77 (c) 3X+2Y ~ N( 18, 77) P(3X+2Y<18) = P(Z<(18-18)/77 0.5 )=0.5 (d) P(3X+2Y<28) = P(Z<(28-18)/77 0.5 )=P(Z<1.1396) =0.873 Section 5-5 5-56 Y = 10X and E(Y) =10E(X) = 50mm. V(Y)=10 2 V(X)=25mm 2 5-57 a) Let T denote the total thickness. Then, T = X + Y and E(T) = 4 mm, V(T) = 01 002 22 2 .. . += mm , and σ T = 01414 . mm. b) 0170 . 0 983 . 0 1 ) 12 . 2 ( 1 ) 12 . 2 ( 1414 . 0 4 3 . 4 ) 3 . 4 ( = = < = > = > = > Z P Z P Z P T P 5-58 (a) X: time of wheel throwing. X~N(40,4) Y : time of wheel firing. Y~N(60,9) X+Y ~ N(100, 13) P(X+Y 95) = P(Z<(95-100)/13 0.5 ) =P(Z<1.387) =0.917 (b) P(X+Y>110) = 1- P(Z<(110-100)/ 13 0.5 ) =1-P(Z<2.774) = 1-0.9972 =0.0028 5-59 a) X N(0.1, 0.00031) and Y N(0.23, 0.00017) Let T denote the total thickness. Then, T = X + Y and E(T) = 0.33 mm, V(T) = 2 7 2 2 10 25 . 1 00017 . 0 00031 . 0 mm x = + , and 000354 . 0 = T σ mm. 0 ) 272 ( 000354 . 0 33 . 0 2337 . 0 ) 2337 . 0 ( < = < = < Z P Z P T P b) 1 ) 253 ( 1 ) 253 ( 000345 . 0 33 . 0 2405 . 0 ) 2405 . 0 ( < = > = > = > Z P Z P Z P T P 5-60 Let D denote the width of the casing minus the width of the door. Then, D is normally

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 / 3

mont4e_sm_ch05_sec05 - 5-54 a E(2X 3Y = 2(0 3(10 = 30 b...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online