Entrance Paper - Statistics - University of Hyderabad - Master in Science - 2008, Study notes of Statistics

Download Entrance Paper - Statistics - University of Hyderabad - Master in Science - 2008 and more Study notes Statistics in PDF only on Docsity! POC UUNUUUUOHOHTHH GHEE H EC GEEGCEECEES N-0¢ Departinent of Mathematics and Statistics University of Hyderabad Fatrance examination - M.Sc. Statis Hall Vickel Number Time: 2 hours Max. Marks: marks Parl B: 50 marks Instructions L. Werite your Booklet Code and Hall Vieket Snumber i dae OME: Answer Sheet given to you. Ake write the Hall Tickel Number in (he space provided above 2. There is negative marking. Do not pamble 3. Answers are to be marked oa the OMR answer sheet. following the in- sinctions provided {here upon, 1. Hand over the question paper booklet and the OMR answer sheet al the end of the exanvinaiion, 5. No additional sheets will be provided. Rongh wark can be dane in the question paper ilsell/ space provided at the end of the booklet Gi. Calenlators are net illawed 7. There are a total of 50 questions in part A aud 2B Logether. 8. The appropriate answer should be coloured in by either a bhie or black ballpoint ar skeleh pea. DO NOT USE A PENCIL. SECTION A Jack question carries L mark for a correct answer auch (0S narks for a wean, adaswer. 1 Let Aland 2 be mutually uxclesive (disjuint) events with strictly positive probabilities of occ: - Then . (A) A® and Beare independent, (B) A® and BP are amitually exelusive, (C) PAU B) = 1. (D) P(ALB) = PUTA} 2, In a school there are 200 children born between Ist dartury 1999 and 30th June 1999 (end dates are ineluded). The probability that no two children have the same birthday is (A) u 3. If an event A occurs whenever event B occurs then it is true that (A) P(A) < P(BY) . (B) P(A’) > PCBS) i (C) P(A) = P(B) : (D) P(A) = P(B*) 4. For the two events A and B, the Probability of cach event is at least, 0.8. P(AN B) is in the imtorval (A) 00, 0.3] (B) (0.3, 0.5} (C) (0.5, 0.6) (D) [0.6, 0.8] * 3 5. Suppose AT is the mode and S® the variance of 1 observations: Lf a negative constant a is added to all (he observations, the mode and variance of these observations will be respectively (A) M+a, 5? (B) M—a, S?--a# (C) M-a, 8? (D) M+a, $?--a t if Saboniss) tee AYPOMRH MR AAD AD? M-o&€ (Cia } (Dis 3 16. X is a random wariable with POY > L) = gh and P(X = 0) = 2. Suppose ¥ is another randene variable for which HOLY -- @)-- = lou and EIN = 1) = 200,000 then £(¥) AA) ca not be determined from the given information (17) is 99500 (Cy is 0 (D} is (OLD , ‘Phe area of a cirele inscribed ins a square (thal is all the sides of the square are Gingents Lo the circle) whose side is 2 cr is (A) a? sqm (1) Y sq ore (C} act se can ' (by = sq cn 10. A and B lwo m x mw matrices, Lhen (A) Rank(A+B)=Rank(A} | Rank(B) (B) Rank(A 1B) < min{Rank(A), Rank(B)} (C) Rank(A+B)> max{Rank(A), Rank(B)} (D) None of the above. 20. A three digit number is abtained by drawing 3 numbers denoted by a, b, ¢ from a purse containing 9 marbles numbered 1,2,...9 with replacement. The scl. of all possible outcomes is (A) {abe | {a,b,c} C {1,2,...,9}} (B) (fa, b,c} | {abo} c {1,2....,9}} (C) {abe | a € {1,2,...,9},0€ (1,2,..., 96 (1,2,....9}} (D)fahe jasbecae (2....9},0€ (1,2....9.¢¢ (1,2,....9)}. 5 BVUVDHVUDYUYOUYYUHOKLHEVEHEHUEECEe ees  P(e alr, {0 lb y For testing a null hypothesis, the level a critical region is Cy if the level Of siguilicance of Le dest. is reduced to ay, Lie Corresponding erivieal repion Ci (A) contains C (B) is contained in C (C) is equal to C (D ) none of the above can he said with corlainily, 23. Suppose you are told that there is a direct relatiouship between the price of a certain trait and the amount of rainfall during the growiug season. [1 can be concluded that (A) Price of dhe finit tends ta be high wheu ( infall is high. (B) Price of the fruit ends to be low when the rainfall is high. (C) A large amount of rain causes price of the [ruit to risc. (DB) A lack of rainfall eauses price of dhe fruil to rise. 24. ‘The limit of th (ao (b) 4 (c) 4 (d) none of the above sequence {an }yz, as 2 — oo where a, = 25. ‘The negation of the statement "Ashok bas read every book in the library’ is (A) Ashok has not read any book in the library. (B) Ashok has nol read at least one book in the library. (C) Ashok has read at most one baok in the library. (D} Ashok has read only one book in the library. OouvuedeudevwTeueuetevuveueeueewuwuvuwuwewwenwwrv vu vd ‘ § vpuewuvuve x a we M-0o¢ SECTION-B correct aaswer od TLG6 marks ier a wrous answer Patel question: carries 2 nines 2G. 20% of the iucividtals ina Broap ean speak Cuglish aad 52% A of the group are females, The percentage of individuals who are either English speaking ur yonale is at most, (A) day qy (C9 G8, (hi 7367 27. AN arrangements of the Wo aunbers t.. 2S a re sate cause The probabiliny that io two eld sunihers ale nest tg eael) other is ’ ] GA) a 1 (B) ar @ a 3 gt (C} (D) 28. A and 8 are independent events with eq 0.75, then qual proba bitities, POA BY = 29. A packet of 5 shirts contains no defective or 1 defecti abilitics 0.5 each. A dealer picks up a shirk from a packet at random and rejects the packet if the selected shirt is defective, otherwise he accepts the packet. The probability that there is a defective shirt in an accepted packet is ve shirt with prob- (A) (B) 5 ~  (C) equal vo 2 (D) at least 2.5 39. ‘The median of the random variable Sale) = { lae"{L—a), Onn 0, otha wise 40. "The joint pdf of two raudein variables X and Y is Ie,u) = { exp{-y]. 0 GO, otherwise Nhe couclivional pal of X given ¥ oy. fLeigt is (Aj Sealy) + { pt 0, ot (B) _flocwet f(aly) = { 0, otherwise (Cc) ’ + _f exp{-2}, 2>0 Fly) = { 0, otherwise (D) flaly) = { rexp{~a}, a> 0 0, otherwise 10 A whose pil is given hy M-0€ LPF 8A oR a # . a Ha o © aa * s a V9 9 9! Ci. a £9 Mf! © a S . ® Huu esuusbveuvvevussesud “Ly uUG vos N-0& AV. "Phe random variable XY follows exponential distribution wid mean }. Then (A) P(X <2) > PIX» 2) (B) PIX <2 < P(X say (C) PX 42. X,, Xy is a random s ample from the normal population with mean tt and variance p?, Then unbiased estimators for jeand p? respectively are (AJ2E%% and (Lug X2y! (B) 2% and Xi . Oe iy fee Os fry { 0, otherwise whore @ £0, Let NX), Ne... -- Xoo be a random sample fron XY. The maxi- mum likelihvad estimator of @ ig (A) 5 8 X, (B) NUS, XP (GC) max{ XP NF... xB} (D) maxX, Xp 44. XNg.. Xn, with mean 0 and v: four given Leluw is is a random sample from the normal dist ribution 22. “The best tinbiased estimator for a2 among the (A) Ean? fe Sei ad il  (By Layce Vos ute 1+ (C) Siviey a (D) PATAAG 45. Let XX, with incan ys Hy +X, be a random sample aud variance 1. The most powerlt > Ho is reject Ay if for a suitable (A) Rek from the normal distribution ul best for £4, : (= fu against constant & (B) F>k (CVX 4k (D) None of the above 46. Let X is a Poisson distr ibuted random variable with uiean 2, then A{2*) (A) does not exist {B) is exp{2} (C) is exp fa} (D} is oxp{g}. 44. There are 20 slips ina bag mumbered 1,2, without replacement, the prob: most 7, the next, sinallest equal (A) suictly less than g +++ 20. Three slips are taken abilily that the smallest of these three is at 40 8 aud the largest is al loast 12 is (B) ut least aq but lesy than Z #9 An 8 Of LA wet cemmat lemeelf Mees iwi ioral iva iment nwa itl oe 6 @ oneoeene O49 a a, PALA 99 9 9