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Closed book aud notes, 0 muures,
1, Trae or false, (for each, 2 potmts if corres, L point if bet blank.)
fa} (t) Po Por every random variable ¥, "X=2" amd *32.X <4" ore mutually
exclusive.
iby T &) Por every random variable: %, “A is alsoan ever,
fe) T E ch? = 90,
a(t) PF By dedinition, Bernoulli tials are independent of each other,
o T@ For every random variable X, this expression is true: VOX) = B(X?) - py.
inf) F Pocevery random variable X, Fyic) = P(X S20) for every real number x.
ta) T(E) Porevery mndom variable X.fyls}= PAX =,
inp TH the “eoatinucas uniform” distribution is cewinncws in the sense that tho density
function has ma discontinuities. (That is, there are no “seeps” in the density
function.)
wofiira dinanual experiment is an experiment compased of n Remoulli trials.
2. Fill in the blanks.
The Dine mi distribution sswers questions about the number of
36 “ successes inn Beerinalli trials,
ib) The 2 Gendles © distribution saswers questions about the number af
Bermaulli cals uncil the first success.
The Megat! veltia Iribution answers questions about the number of
Bernoulli tials uni) the eth success,
ie
jp,
(dy ‘The tei ison distribution answers questions about the umber of
counts in an interval,
The h eA Ve disinbuthon answers questiods about the number of
suecesses in a sample of sige. from # population of size N containing K successes,
ie
Exam #2b, Fall 1909 Page Lot 4 Schmeiser
(ene Key
3. Result: IW Xis continuous, then Plo <8 2.6) = Fyih)= Fyfe),
Prawide a cesson for each line of the proof,
IE 230 — Probability 4 Statistics in Engineering |
362) Pa SXSH)SPN=a or a<Xsb) _ Semesyent
=P(X =a)+ Pia ¢X 25) rawr tas éxefusive
=Fla <X 2h) P&f=e) because irr cocfinumnt
= PIX s4)-PIX sa) Mee Uo ne nes" 2" ¥ fh”
= Fb — Fyfe) definrtinn of ed f Fe
4. The propron,X, of people who respond to 2 cen mi-oder slicaion has density
junetion
Fels) =o (62) if s%s1
and zero elsewhere.
4 s (a Find the value ofc. ¥ t
? J‘ elnea)en feral),
: +2) (2° %
: hecanre (Oe 32 1.
= c= a = = Ve
a
& +f y (b) Sketch the density function, Label and scabe all axes.
bs a
te
4 te)
¥ ae -
9
oa 1 “F
Exam 02h, Fall (999 Page Zof 4 Sehmelser
