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Unformatted text preview: Math 351 Exam 2
W.T. Kiley December 1, 2006 Clearly show your work and answers. Follow the Honor Code. (/Z)1° X is normal with a mean of 100 and a variance of 16. Find:
a) the probability that X is between 98 and 102; b) an interval that has .9 probability of containing X. i ‘ WW 4) 29/755 MW) 2 27:94 2:5) a éZ; “’5 19 ﬂ: P{—/,é7;:2 5/225): Hrwﬁé’f XMf/MQ 6’ [7) 2. Y is the mean of 25 independent values cf the above X.
Answer the same 2 questions about Y. Z = 1:122 Wax, é/ﬂﬂ; a} was?
.8’
00 PKVs/f/o 2) = {9(3sz 2 52;) r, 773;: M42. M9: PHMSE VT? sue/(j
= P[ was xv 5 MIKE/é] (/2) 3. X is uniform on [2,2] and Y = X . Find:
a) the p.d.f. of Y; b) the probability that Y is less than 2. W
50 F/g) 7~ 5;, 91 “ff/9);;I/Z‘) rad/7765 : y
< I b) 4. The joint p.d.f. of (X,Y) is e for 0<x<y. Find:
a)the p.df.for Y; b)the erop roaiiaisbbltythtY sesl sthanl;
cec)th onditio na..lpdf.for X,giventhtY= y;eed)th exevapectd auel o,fXgive nY= y. <I?)5.eThjointp..df.o o,isf(XY) 9x 22y for o< x,.y<l Fi nzd
aec)th variance o;fXandY b)thejoi n..tpdf.o er= XYandV= Y, c)the e.pdf. o.fU a) {( W)/ W WW4
5(X7>»jofo’f¢gz MM I f ¢g74ﬂ)/o/gzj%
[J;:/x/JA][Jy {My} MMM
4., /J( y): 500/} ENE/V) p X’V;/l/,a¢f «ﬁg; [’2 % ’4' ef/an M wa =~
0 «0:3 31:07 4’ ”W €M’ZM/ ﬁeﬂ’Aa/EMHJ ...
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