mont4e_sm_ch03_sec08

# mont4e_sm_ch03_sec08 - 3-96 Let X denote a geometric random...

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

Section 3-8 3-97. X has a hypergeometric distribution N=100, n=4, K=20 a.) ( )( ) ( ) 4191 . 0 3921225 ) 82160 ( 20 ) 1 ( 100 4 80 3 20 1 = = = = X P b.) , the sample size is only 4 0 ) 6 ( = = X P c.) ( )( ) ( ) 001236 . 0 3921225 ) 1 ( 4845 ) 4 ( 100 4 80 0 20 4 = = = = X P d.) 8 . 0 100 20 4 ) ( = = = = N K n np X E 6206 . 0 99 96 ) 8 . 0 )( 2 . 0 ( 4 1 ) 1 ( ) ( = = = N n N p np X V 3-18

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

View Full Document
3-98. a) ( )( ) ( ) 4623 . 0 24 / ) 17 18 19 20 ( 6 / ) 14 15 16 4 ( ) 1 ( 20 4 16 3 4 1 = × × × × × × = = = X P b) ( )( ) ( ) 00021 . 0 24 / ) 17 18 19 20 ( 1 ) 4 ( 20 4 16 0 4 4 = × × × = = = X P c) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 9866 . 0 ) 2 ( ) 1 ( ) 0 ( ) 2 ( 24 17 18 19 20 2 15 16 6 6 14 15 16 4 24 13 14 15 16 20 4 16 2 4 2 20 4 16 3 4 1 20 4 16 4 4 0 = = + + = = + = + = = × × × × × + × × × + × × × X P X P X P X P d) E(X) = 4(4/20) = 0.8 V(X) = 4(0.2)(0.8)(16/19) = 0.539 3-99. N=10, n=3 and K=4 0 1 2 3 0.0 0.1 0.2 0.3 0.4 0.5 x P(x) 3-100. (a) f(x) = / x x 3 12 24 3 36 (b) μ=E(X) = np= 3*24/36=2 V(X)= np(1-p)(N-n)/(N-1) =2*(1-24/36)(36-3)/(36-1)=0.629 (c) P(X 2) =1-P(X=3) =0.717 3-19