This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Statistics 20: Midterm 2.
Spring 2007. Name: \L Q/
Student ID: Instructions You have untii 3:30pm to ﬁnish this test. You may use one sheet of notes
and a calculator. Please show your work and circle your answers to each question. 1. Suppose X and Y are independent random variables such that XN ~Bin(5 1/2) and
Y~ Bin(10, 1/3). Find sd(X Y). 25~<i()( ~27) lwi XWafY We; 2. Suppose I randomly pick 5 cards with replacement from a standard deck of cards.
What is the probability that three of the cards are Kings? ,ﬂ;% I403; NBE(§,%‘L
(P( ii 56 14230:) f <2 2%? :3” 0.003? {11:31 ‘ 3. Mr. Smith’s gardener is not depe2ndableg'the probability that he will forget to water the
rosebush during Smith’s absence is g. The rosebush' 1s in questionable condition anyhow; if watered the probability of its withering IS 2, but if it is not watered, the probability of
its withering is %. Upon returning, Smith ﬁnds that the rosebush has withered. What 1s the probability that the gardener did not water the rosebush? 49170111 wary172), , cpwaev) V3 ‘ ?( N0 Waler (willed; w ;C3/\>(2 3 W 17(wll’LA I No WRAMM waleA +lemMl 111M)? Width“ 34. ‘93 ,1 4. Suppose that a random variable has the following density 1/3 for —1 < a: < 2
otherwise. f(w)= {0 Find the probability that this random variable will be less than 0. Find the variance of
this random variable. 5. 7 The probability that a man will. hit a target is g. If he shoots at the target until he
hits it for the ﬁrst time, ﬁnd the probability that it will take him 5 shots to hit the target. 6"" Sinis te are :1 4mg 2,. m  HM w (W ) 6. The lengths of full—grown scorpions of a certain variety have a mean of 1.96 inches
and a standard deviation of 0.08 inches. Assuming that the distribution of these lengths is
normal, ﬁnd the probability that a fullgrown scorpion has a length of 2.20 inches or more.
Also find the probability that a full—grown scorpion has a length of at least 1.8 inches. L FIN/mt, @0713”) 7 a 2221mm : _ g"
P(L’Z'Z): P( 050% . 000’? > ZNA/[é‘i‘] ‘Pimﬂt W22” W 4533} (3617729 7. Let X1,. .,X20 be independent copies of a random variable that is normally dis
tributed with expected value 55 and standard deviation 10 Let Xm Jifoﬂﬁm. Find
P(.X > 56). X AMBER '0 > E32: 51;? §9Q(§)3 ma zip/Mos) 8. T03 11110tme3 .eLtYr cordithenu nur‘nber 0efhds nersosthﬁth and
letXr ordth:0 numerb o'fhe as1d tnhe 13311615513363.0111th P1(Y= 2)B.11dP(X:a1).
Are X311in 11de ned nt?Sh0wy0 easo ning? WBM '4) x0334 1/3) I
P(Y'gst 261.4! L2>é_ ' a : 0131(‘1
VD“? iglG P '" ‘0705f3f 7 I —o  0 ‘ ‘ I I ' /
ﬂénggm :fé X3: are. View" ‘WM (102) dY~ Bi n(1,0.4) A130 suppose P(X= 0&Y= 0)= 048
HX=oeygn=om
" P(X=1&Y=0)=0.12
P(X=1&Y=1)m0.08 Coueemptth O_fX+2Y MIX UP?) (03%“) 01132
WK [03PM 13 (~:(03>00 032 KM JL '7? . MAN 3 (021(06') on) I 3 J
PX,.[W )L;\r £02.) 01‘):— 003 ‘ $W ...
View
Full Document
 Spring '08
 anderes

Click to edit the document details