347.2003.3f.sol

347.2003.3f.sol - NAME E 5 j ' MATH 347-10 Exam #3f...

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Unformatted text preview: NAME E 5 j ' MATH 347-10 Exam #3f November 24, 2003 Page 1 of 4 Show all work. 45 points maximum score 50 minutes allowed The test is printed on both sides of the paper. 1. (9 points) A continuous random variable, Y , has the distribution 0, y _<_ 0 function at the right: 2 F‘dP1<Y<24 F(y)= 0125)) ’ O<ysz a. m r( — -)- 0.5(y—1), 2 < y s 3 b. Fll‘ld Pr(YS 2.4 | Y> 1). 1’ y > 3 c. Find the density function, f ( y ), of Y. W MIC! aw): Foam—Fa): :0‘5'(&-L(-()—?0~’9~9(I)" '- 0.7"0\U-$'=0,5’75’ w (é) ?(Y§_.;z.ql‘(>1): PCYékqt‘bL) P(‘/7 1) 1-, [’(LLVeax) i~ P(‘/41) I i—-F(1) "f:;;}=6£657 F\h,_x\~_~§____\\_#_\‘_’//F\\\\ 0.190 0< z. V2 flvl 0’?) 9~ <§£3 0) (‘7’>3 MATH 347-10 Exam #3f November 24, 2003 Page 2 of 4 2. (6 points) Find the expectation of the continuous random variable, Y, whose density function is y, 0 < y < 1 f(y)= Z-y, ISy<2- 0, elsewhere ECU: JPIyDJxa. '4. 2:04? ‘1 (7%"? *f/Le/(a'ypza +5245 ll 3. (6 points) The amount of time that a watch will run without having to be reset is a random variable having an exponential distribution whose mean is 120 days. Find the probability that such a watch will have to be reset in less than 24 days. LI Yiwbrlobj§wflmmmzabfigimt \ 4, __L.. ‘WILO 77“" { SwaU-ULW 52(9): {/90 8 J 1y>0 0 ) WM ‘ NAME ii 5 Z ' MATH 347-10 Exam #3f November 24, 2003 Page 3 of 4 4. (6 points) If Y is a normal random variable with a mean of 17.1 and a standard deviation of 3.2, find P(l4 S Y S. 25). Use the supplied normal probability table for this problem and show how you standardize Y so that you can use the table. You may not use the statistical functions on your calculator. [Hint Draw the picture] \//\1 (3L1)?r) M i: 1%: NN/aj I), 3‘; Y’WJ ¢ Jr— ['21 3‘). h 3‘; 5. (6 points) A certain professional society wishes to set the passing grade on an examination so that only 33% of the candidates will pass. If the examination scores are normally distributed with a mean of 70 and a standard deviation of 10, at what level should they set the minimum passing score? Use the supplied norrrial probability table for this problem and show how you standardize the scores so that you can use the table. You may not use the statistical functions on your calculator. M 7’: (kWan Wswmfle Mw‘ fl“ ‘/~ N(702/01),M Z: 72070 Av Mm l)‘ MATH 347-10 Exam #3f November 24, 2003 Page 4 of 4 y 6. (6 points) A random variable Y has the density function f ( y) = e ’ y < 0 .Find the 0, elsewhere moment-generating function of Y. [Read the problem carefully: the support of Y is the set of all negative real numbers] ky4(1—y)2, OSySI 0, elsewhere 7. (6 points) A random variable Y has the density function f (y) = { a. Find k. [Hint: You do not need to integrate] b. What is the distribution of Y (its family and any parameter(s))? c. What are E(Y) and V(Y)? (a) M (fin—01,? QfiWWjfla 7m ol~l>£f M p-1=.;1 W °Z>57 5:3) IL:J&L-M_- 7-’ WWW» ‘ FEW/3) #11; c,_o4_3_,,...._~ __.6_:l_= s’ ,3 VP“ ‘ (df@)1(o<f@+1) ‘(2’)’H7 5'76 O‘OQ‘Q’ ...
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347.2003.3f.sol - NAME E 5 j ' MATH 347-10 Exam #3f...

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