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Pune University - SY BSc (Sem - I) STATISTICS - I : Statistical Techn, April 2010

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Total No. of Questions : 4] P278 [Total No. of Pages : 2 [3717] - 121 S.Y. B.Sc. STATISTICAL TECHNIQUES STT-211 : Statistical Techniques - I (New Course) (Sem. - I) (Paper - I) Time : 2 Hours] Instructions to the candidates: 1) All questions are compulsory. 2) Figures to the right indicate full marks. 3) Use of calculator and statistical tables is allowed. 4) Symbols and abbreviations have their usual meaning. [Max. Marks : 40 Q1) Attempt each of the following : a) Choose the correct alternative in each of the following : [1 Each] i) The equation of regression plane X1 on X2 and X3 is 2X1 + 5X2 + X3 = 10. The value of b12.3 is : A) 5/2 B) 1/3 C) 2/5 D) 2 ii) If X N(10, 4) then p(X < 10) is equal to : A) 0.10 B) 1/2 C) 0 D) 10/4 iii) If X NB (4, 2/3) then variance of X is : A) 4 B) 8/3 C) 3 D) 1/4 b) State Whether the given statement is true or false in each of the following : [1 Each] i) If X NB(k, p) then mean > variance. ii) Let X N(10, 10) and Y N(10, 10). If X and Y are independent then X Y N(0, 0). 2 iii) b12.3 b13.2 = r12.3. c) Define standard normal distribution. [1] d) State lack of memory property of geometric distribution. [1] [1] e) Define partial correlation coefficient r12.3. f) Give a real life situation where multinomial distribution can be applied. [1] P.T.O. Q2) Attempt any two of the following : [5 Each] a) State p.m.f. of geometric distribution with parameter p. State its mean and variance. Also state a real life situation where it can be applied. b) Define multiple correlation coefficient R1.23. Also state its properties. c) There are 30% of the donors of blood group A. A blood bank needs 6 donors of blood group A. What is the probability that 10th donor will be the 6th one of blood group A. Q3) Attempt any two of the following : a) [5 Each] 1 . State its variance and distribution function. Also state its lower quartile. Define exponential distribution with mean b) A box contain 5 red, 5 blue and 4 black balls. Four balls are selected at random with replacement. Find the probability that the sample contains one red and at most one blue balls. c) Let X N(100, 25) and Y N(200, 16). If X and Y are independent r.v.s. find p(290 < X+Y < 295). Q4) Attempt any one of the following : State the equation of regression plane X2 on X1 and X3. Also state the formulae for b21.3 and b23.1. [5] A fair coin is tossed 400 times. Using normal approximation find the probability of getting number of heads between 190 and 205.[5] i) In an examination, 33% students secured marks less than 40 and 45% students secured marks more than 80. Assuming marks secured follows normal distribution. Find mean and variance of the distribution. [5] ii) b) i) ii) a) The probability of successful launching of a rocket is 0.85. Find the probability that fewer than 4 attempts will be required to make a successful launching. [5] vvvv [3717]-121 2

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Additional Info : S.Y. B.Sc. Statistics (Semister - I), STT - 211 : Statistical Techniques - I (Paper - I) (New Course), Pune University
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