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Unformatted text preview: Statistics 20: Midterm 2.
Spring 2007. Name: \L OJ
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 X N Bin(5,1/2) and
Y N Bin(10, 1/3). Find sd(X u Y). . ' “€524— (Xra 1* iv“; XwafY '3’ "4., m; 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? 14; % I403; 425(6) jg}; ’P< 56 Mfkgﬁjgs g L 4})
Bl‘zl I f M r: 0.003? ,' mil ‘ 3. Mr. Smith’s gardener is not dependableg'the probability that he will forget to water the
rosebush during Smith’s absence is The rosebush is in questionable condition anyhow;
if watered, the probability of its withering is %, but if it is not watered, the probability of
its withering is Upon returning, Smith ﬁnds that the rosebush has withered. What is
the probability that the gardener did not water the rosebush? PC No gfg, ﬁiwﬁeyv l; '6
ﬂawlm Wands? I Mam/LIME») =‘/Z
343p lNa ' P(No War/Cr) ﬁ__ﬂ_______________________ " VOW walerlwfﬂwnl Pl I C34) ( aw , z:
1 twin4 IMo WMMW walev\+Pliim“l“‘“)?(WWh 4. Suppose that a random variable has the following density  _ 1/3 for—1<a:<2
Km) _ { 0 otherwise. 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 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. ff” g.“ ‘~ ‘ i: b m; ﬁg 4 LIA ' 1 '{IM
(Prob "’ ( a) t a)
6. The lengths of full—grown scorpions of a certain varietyr 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 .JN/mt, Q9 075,3) 7 . " : ' 23'2‘W10ﬁmé : ' P(L’ZZ) M. 050%" . 0‘00]? ’ QNA/[e‘i] that)? W22 “wt; 0617719"? 0. oz” ‘ l
7. Let X1, . ,Xgo be independent copies of a random” variable that is normally disu
tributed with expected value 55 and standard deviation 10. Let 7 m Find
PC}? > 56). ' X; we no , a: 5;, 4m» ma ' zit/MA) f 8. T055 3. fair coin 10 times. Let recorgthe' nur‘nber 0f heads in the ﬁrst 6 tosse s and let X record the number of'heads in the iaét‘ﬁ tosses. Compute P(‘Y = 2) andPOI 51). Are X and Y independent? Show your reasoning? magnum, x MENU/Vs) 6! LG 6"
176/723“: 2M! 2) : L911" 0 lgwi mx=0&y=m=e%
P(X=0&:Y=1)=0.32
" P(X=1&Y=0)=0.12
P(X=1&Y=1)m0.08. PKX"°)P(‘/w> :: (033(06): GAE?
@[X’ODPW‘A :I (0,3){0‘1} 032
Pom—m = (10.21) (as). 0.12
mxmw Low): W X+ L\/)r darXaF Wain!) ...
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This note was uploaded on 04/02/2008 for the course STAT 21 taught by Professor Anderes during the Spring '08 term at University of California, Berkeley.
 Spring '08
 anderes

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