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! University of Hyderabad, Entrance Examination, 200% MSc. (Statistics - OR) Hall Ticket No. Time: 2 hours Part A: 25 Max. Marks: 75 Part B: 50 a Instructions 1. The OMR sheet contains space for answers to 100 questions. Answer Part Ain 1 to 25 and Part B in 26 to 50. Ignore the remaining spaces. 9. Fill in your hall ticket mumber in the space provided in both the OMR sheet and on this page. ‘ 3. Calculators are not allowed. 4. Each correct answer in Part A carries 1 mark and each wrong answer carries O nr So do not gamble. 5. Each correct answer in Part B carries 2 marks and each wrong answer carries 06s Eman 6. There will be no penalty if a question is unanswered. 7. Answers are to be given on the OMR sheet provided. we w a ly < / eater 8. The appropriate answer should be coloured in by either ‘black ball pointy pen orablack-sketeh-per. DO NOT USE A PENCIL.  18. tel C= {(x,y); xy eRe vo -2xty?-ay > 4}, Cis {A] the boundary of a circle (2) the interior of a circle {C) is a closed disc (D) the exterior of a circle 19. Tne function f(x) = 5¥-4%-3%42", then for F(x) = 0 I (A) x (C) x O and x = 1 are solutions [B8) x = 0 is the only soluLlion a1 and x = 2 are solutions (D) has no solution 20. The random variable X has pdf fx) = |x], -1<x<1. Then (A) E(X) > 0 (B) EX) < 0 (C) EX = 0 (DB) POO) > 2 x 21, The value ef | wa dx {A} does net exist (B) is oO (Cc) is <6 (D) is > 0 Answer Questions 22 and 23 based on the joint probability distribution of % and Y given below. 0 0 va 1/4 1 1/6 1/6 1/6 22. P(X = 0) is (A) 1/6 (B) 1/3 (C) 5712 {D) 142 23. P(X = 1}¥ = 0) is (A) 145 (B) 275 (ct) 375 (D) 445 24. X N(O,1) <a, <a, suppose P(X < ay) =a; P(X = ay) = ay then Plray < X < a ) is 1 (A) 5-0 (B) &-%y (C} a ta, {(D) = 25. The moment generating functions of two independent random variables x and Ky are M(t) and Mot) respeclLively. The MGF of Xy +2, is (A) Hy ft) + 2M, (t] (B) M(t} + ML O1) (c) 2M, (tM, (t) (D) My (t)M, (at) + T-h 26. 27 28. 29, 30. 31. 32. SECTION~-B X is a random variable with Poisson distribution, P(X=1) = 2P(X=0), then P(X=2) is (A} equal to P(X=1) (B) twice P(X=1) (C) equal to F(X=0) (D) 4 times P(X=0) From n distinct objections, the number of subsets of size 3 is twice the number of subsets of size 2. Therefore (A) n = 10 (B) n = 12 (Cc) n=8 ()) information given is not sufficient to detcrmine n. A group of 7 friends, 3 girls and 4 bays go to watch a film, they have tickets to seat numbers 7 to 13 (all in a row), they decide that only boys will sit on seats 7 and 13. In how many ways can these 7 friends be seated with the given condition? (A) 720 (B) 5047 (C) 24 (D) 1440 pe vy Bo) = 0.7, P(A) = 0.4, PCB) = 0.5, then P(A UB) (A) is 0.9 (8B) cannot be obtained from the information given (C} is 0.6 (D) is l ayn ae = -A4, a478y = 5, ag7 ag = 9, with this information on aya, and ag (A) both mean and variance can be obtained (B} variance can be obtained but not the mean (C) mean can be obtained but not variance (D) neither mean nor variance can be obtained There are 10 slips numbered 1,...,10 in a bag, two slips are drawn, the set of all possible outcomes S is (A) 1.0.5 40} (B) (4, )s LJetl,.. 203) fe) (isd); ded @ (eee 20M (D) A, Ss MeL € AT. TOW) fod = cel! -wexem, what should ¢ be go that fy is 2 probability density function? (A) 2 (B) 1/2 tc) 174 (D) 2 4 — 33. 34, 36. 37. 38. 39. 40 Two distinct numbers are selected from {1,...,10}, the probability that the larger of the two is more than 50 is (A) at most 1/4 (B) more than 1/4 but not mere than 2/3 (C} more than 1/2 bul not more than 2/3 (D) more than 2/3 The first and second raw moments of a random variable X are 12 and 100 respectively, Which of the following is correct. (A) This can never happen, {B) This can happen if X has binomial distribution (C) This can happen if X | N(p, o7) for some choices of (u, 0”) (D) this is true for ¥_ P(12) X and Y are two random variables taking values 1,2,3,4 with the foi = 1,234) P= 1) = 5/10, PCY = 2) = 1/92, P(¥ = 3) = 11/92, P(Y = 4) = 5/16 then following distributions P(X = i) = (A) EX = EY (B) EX > EY (C) P(X>1) < PCY>41) (D) EX < EY The correlation coefficient between X and Y denoted by Pyy is 0, which of the following statements is always true <0 50 (py iy (A) py > 0 (B) ¢ =O (C)ey _ X,-¥ x2 ,¥" X,7Y The probability that among k randomly selected digits, the digits O and 1 are not there. ay Ky10% oa) @®i0® cep ako ony tt In every scanning cycle, a radar tracking a space object getects the object with constant probability p. What is the probability of detecting the object in n cycles? n (A) p (B) 1-p' (©) (-p)™ (D) 1 - G-p)™ An unbiased coin is tossed until a head is obtained. If MN denotes the number of tosses required, what is P(N > 1)? (A) 142 (By 1 (c) 174 ()) 178 L Let X be a random variable such that P(X = i) = tm «for i= o-n, -ntl,...,71,0,1,...n. What is V(x)? 2 n 2 2 n{n+l} n’(nt+1) 2) (n+1) n@{n+1) (Ay 3 (By ——— (C) (D) SS 3