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Unformatted text preview: STAT511 Exam 1 Summer 2008 (50 pts) I. Multiple choice 1. Which of the following is not correct? \\ NOWC 0t @Nutually exclusive events must be independent events
Co({ectB PM U B) 2 PM) C Axioms of probability say that for two events A1 and A2 are mutually exclusive,
Cﬂlledc we have P(A1 U A2) = P(A1) + P(A2). D None of the above is correct 2. P(A1) = 4/5, P(A2) = 1/5, A1 and A2 are mutually exclusive events. Suppose we
know P(BA1) m 1/10 and P(BAg) = 1/5, ﬁnd P(A2B). Bayes) 3. X N E‘pr = 5), What is the probility of X > 3? _ 1 — 6—15.
B 1 — 36*15
C 36—15 eer 4. A deck of 52 cards, take 4 out Without replacement one by one. We saw that the ﬁrst
card is a club, now what is the probability "that second is a heart? 132
C 5251 D None of the above
5. X N U(2,5)1 what is E(X2)? A E
13
C i
D None of the above 6. For the standard normal distribution, which of the following is not correct? A The density function is f(z) m ﬁe“22/2,.—m < z < 00 B Mean is 0 and variance is 1,
C It is hell shaped @t is a discrete distribution what is the probability that there are at least one red ball? ._ 8. ,Every second, there are 3 cosmic rays hitting a spot on earth. Let X = the number
of cosmic rays hitting this spot within 40 seconds. What is P(X = 2)? this is l
E
E
E
7. A box contains 10 balls, 5 are black, 5 are red. Take two bails out with replacement,
a Poisson process with 04 = 3) * "3
A 1 — 9;!
B 1 — 3—120 — e120  120 C 3120(1 +120 + 1202) e— 120 1202
2! 9. X is a continuous randomﬁ variable, which of the following is not correct? @X is a function. B We can find P(X = 2:) for all possible 3 values and then we know the distribution. C X 2, 2X or any function h(X) are also random variables D There are inﬁnitely number of possible values that X ' can take on. 10.
1002299, 0 < a: < 1; f 2 { 0, otherwise.
Is f a density function? Why? I
A Yes. Because f(:1:) 2 0. B No. Because f is not symmetric. ‘©Yes. Because f 2 0 and f(;t)d:r 2' 1.
D None of the above II.(16 pts) Among 5 million married women older than 45 years of age, 1% have no
kids. For 1000 women, let X = the number women who have no kids. Find the following: 1. (2 pts) What is the exact distribution of X ? 2. (3 pts) Among the 1000, what is the expected number women who have no kids?
3. (3 pts) What is the variance of X ‘? 4. (8 pts) Find the probability that there are at least 3 women Without kids using appmmaﬁon‘ F 3‘ 045 nr/mo . X MMM’) a rafﬂe} Me 14/0 2: Mia (0.95) : 9’50
ﬁx : WP/ﬁﬂ :: W/M W‘s 7H}, 3‘; :: 9 9’71; WW3) X: 10/9545? WW: {EL/$0955
:IrIDOﬁSZ} : XL
1‘ P szz) b>(xzr)~'P(/V:03
:1 — Em 7oz euro/7+ 555.47 "2‘? M 0!
#8 000/29 #2me : 12/0/770/ 51/0 4‘64, (16 pts) III. Let event A 2 a Purdue student has to take a math exam, B = a Purdue
student has to take a stat exam, 0 = a Purdue student has to take a chemistry exam. We know that P(A) = a, 13(3):— b, 13(0) = c, and P(AﬂB_) : 2:, P(Aﬂ§) = y, £1403) = 2,
P(AﬂBﬂC)=d. Find: C E C l. (8 pts) Given that a student has a stat exam1 what is the probability that this
student has to take all of the three exams?  2. (8 pts) Given that a student does not have math exam, what is the probability that
this student also has no stat exam? 6 WW 3/): ) 8) ":— PL—ﬂﬂﬁﬂd : ’ <
' PKB) @ awe9m): PM): l—P//4(z/3) .
* PO46) We) MP/ﬂ) _: W we) ' i (18 pts) IV. Measurement error of some machine is a normal random variable with mean
2 cm, standard deviation 5 cm. 1. (5 pts) What is the probability that the measurement error is negative?
2. (5 pts) Find the 96th percentile of the measurement error. 3. (8 pts) What is the probability that the absolute error (absolute value of the error)
is greater than 5 cm? © :p[Z<'__0'LD : OrBHL}X/VN(2}6) E 0'2
2:0,:2 :uLf
S
(2)) EASE.
Y;/m—}Z.U'
:Q+WS%5:(0075 he
2%,? @ PUXDEJ :3 P(>(<’§ or X>53
I WXC'Q +P(X‘> S) «5
;: 'P(Z<~w)+?D(Z77.Lg 2: _gh9:_,vti
:(Qrgﬁ(‘l'ﬂ 5
tr CM WM? :W‘W END OF EXAM ...
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 Fall '08
 BUD

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