Q2_Math308_608

Q2_Math308_608 - Quiz 2 Math 308/608, January 29 1....

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Unformatted text preview: Quiz 2 Math 308/608, January 29 1. Consider a. population consisting of N = 3 values: —2, O, 2. The sample of size n = 2 is drawn from the population. Calculate the sampling distribution of the mean, its mean ELY), and its variance V0.11?) if a. the sample is drawn without replacement. b. the sample is drawn with replacement. 2. Consider a population consisting of N values. The sample of size n is drawn from the population. Show that a. . 2 W l Var-(J?) z t; if it is drawn Wt replacement. b. 2 Vere?) = :~(1~ 3%) if it is drawn without replacement. Hint: For simple random sampling without replacement, for :7 aé j CW(X1,XJ) = — N QUCLE Mq’rk 508/608] ganmufl/ 2‘? A/=2> VQIUQS! —2/91 60115.95 @3leer fix“) (—2 03 7:4 P(3?=—I) :55 J (- 2’2) i=0 Pai=o>cg . 3,. K (o )2.) 36:1 Pki=0=b —, o : / d :- E(7<)'( 1)P(;<=‘)+O'P(X‘°)+f ka=Iy=i(—1+o+\) o _ _ L — 1 ti : Vax<7<)=(*I*O)ZPkY-~I)+(ow) P<><=o)+u—o> PW ) I (‘9 b) Ki!) {1'9‘Qctmen4 ‘- - 'I/ (~2 ~2) 7(=-—z POW-23m; (1:07 33:" flit-0:31 ('2, 2') it") 0):: /q __ ‘:..{ a Z (0)02) gco P(X=‘\*/q (o, ) 11 Pm: 2):? (o, 7,) X q (2 "2) X: 0 Amiga) " d x (2/ X11 I“ If: I “129 H :21. o . L K -"' 1'. ‘ . i .a— t»... - ‘2 E'_5‘+1*Z+2 *0 ax) qL2+QU +0 L: 14/ Vang): ('1' (41- f-Z+ 6.5+- |-2+4)=§g§+lc) '2: —O (1) NHL. {QP\0\C€,Mtfi+ mfl L 1. G i I . : —-* : =LJEVWKXKH1:RV“6 1 h (3‘ S/fnlk Cm/KXK-l :3 LL K ‘ x‘ ( ( +kgex e/fvncrfi‘ \‘r S \DcHer +° Pt RDW'R’HQW3V gplmtemcfi+~ 1c Back 3m Pablemig We. caudci Ul-S'Q VCR/(2): N“! 6"”: ($409+ (03:0)1+ K? -°>L = 86 Rflfi mines ant Let/L . Tkm 0x) WH’L\0M+ /e.plc1ce,men+ 8 _.. Z3 — 8/3 .— gi :2. —- - 1 : 2/ VO\((X):"2:U a)" z a .3 /‘ SOW'IP’L 5‘1"}: \ P§Pq|cd~lm 5:51 W - M b) WHR (Qflcice nan-F -8/5 4 VQWKR>~F= é Sampk Silk n ...
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Q2_Math308_608 - Quiz 2 Math 308/608, January 29 1....

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