B. Com. (Part – III), ADVANCED STATISTICS (Paper – I), 2014 Question Paper Solapur University Question Paper

Solapur University Question Paper B. Com. (Part – III) (Semester – V) Examination, 2014 ADVANCED STATISTICS (Paper – I) Day and Date : Wednesday, 2-4-2014 Max. Marks : 50 Time : 3.00 p.m. to 5.00 p.m. Instructions : 1) All questions are compulsory. 2) Figures to the right indicate full marks. 3) Graph papers will be supplied on request. 4) Use of soundless calculator is allowed. 1. Choose the appropriate alternative from the following. 10 1) One dimensional diagrams are prepared on the basis of a) height b) length c) both a and b d) none of these 2) In multiple bar diagram, the width of different bars is kept a) different b) identical c) both a and b d) none of these 3) A group of some or all of a given number, number of things without considering their order is called a a) permutation b) combination c) both a and b d) none of these 4) All possible outcomes of a random experiment forms the a) events b) sample space c) both a and b d) none of these 5) When the events are mutually exclusive, than P(A ∪B) is equal to a) P(A) +P(B) b) P(A) +P(B) −P(A ∩B) c) Both a and b d) None of these 6) If A is an event and A its complementary event, then a) P(A) = P(A) − 1 b) P(A) = 1+ P(A) c) P(A) = 1−P(A) d) None of these P.T.O. Seat No. SLR-B – 46 -2- 7) The conditional probability of an event B on the assumption that another event A has actually occurred is given by a) P(B / A) = P(AB)/P(A) b) P(B / A) = P(AB)/P(B) c) P(B / A) = P(AB) d) None of these 8) Two events A, B are said to be independent, if a) P(A/B) =P(A) b) P(B/A) =P(B) c) Both a and b d) None of these 9) Probability mass function is always a) 0 b) greater than 0 c) greater than equal to 0 d) none of these 10) When X is a continuous variable, function f(x) is called a) Probability mass function b) Probability density function c) Both a and b d) None of these 2. a) Explain the meaning and construction of Pie diagram. 5 b) Find n ; if C 55. 2 n = 5 3. a) What is the relation between permutation and combination ? Find r ; if nPr = 24 nCr . 5 b) The following data relate to the enrolment of students (in thousands) in university in difficult faculties. Present this data as a multiple bar diagram. Year Arts Science Commerce 2008 20 10 12 2009 25 12 14 2010 30 15 14 2011 40 20 25 5 4. Attempt any one of the following : 10 a) Define the term : i) Sample space ii) Probability of an event. For any two events A and B, prove that P(A ∩B) = P(A)⋅P(B/ A). b) A random variable X has the following probability distribution. Values of X : − 2 − 10 1 2 3 P(x) : 0.1 k 0.2 2k 0.3 3k i) Find the value of K ii) Obtain P(X < 2) and P(X > 0). iii) Construct the distribution function FX(.) of X. 5. Attempt any one of the following. 10 a) Define : i) Joint probability mass function of X and Y. ii) Marginal distributions of X and Y. iii) Conditional probability distribution of X given Y = y. b) For the following joint probability distribution of X and Y. P(X = x, Y = y) = ; 24 x + 3y y 1, 2 x 1, 2 = = Find : i) Marginal probability distribution of X and Y. ii) The conditional probability distribution of X given Y = 2. –––––––––––––––––

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