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Pune University - SY BSc (Sem - II) STATISTICS, April 2010

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Total No. of Questions : 4] [Total No. of Pages :3 [3717] - 214 S.Y. B.Sc. STATISTICS ST-222: Continuous Probability Distributions - II and Demography P492 (New Course) (Sem. - II) Time : 2 Hours] [Max. Marks : 40 Instructions to the Candidates: 1) All questions are compulsory. 2) Figures to the right indicate full marks. 3) 4) Use of calculator and statistical tables is allowed. Symbols and abbreviations have their usual meaning. Q1) Attempt each of the following: a) [1 ] Choose the correct alternative in each of the following: i) Suppose X follows Chi-Square distribution with mode 6 then E(X) is A) C) ii) 4 6 B) 8 D) 5 Let X1, X2,...,X20 be a random sample (r.s.) from N(25,80) with S2 is sample variance S . Then the distribution of 4 2 A) B) 2 25 C) iii) 2 4 129 D) 2 20 Suppose X1, X2, ..., X10 is a r.s from normal population with mean and known variance 2 . Then under H0 : = 4 , the statistic 10 (X 4) follows: A) N(0,1) B) t9 C) t10 D) t4 P.T.O. b) State whether the given statement is true or false in each of the following: [1 ] i) For t-distribution with n degrees of freedom (d.f.): Arithmetic mean = median = mode = 0. ii) In a pair t-test, observations in two samples are independent of each other. iii) With usual notations, the formula to estimate the population for intercensal year is Pt = P0 + (B D) + (I E) . c) Define Snedecore s F- distribution with n1 and n2 d.f. [1] d) Define Chi-Square distribution. [1] e) Give one real life situation where Chi-Square test can be used. [1] f) Define gross reproduction rate (G.R.R.). [1] Q2) Attempt any two of the following: [5 ] a) State and prove additive property of Chi-Square distribution. b) 2 2 2 2 Describe test procedure for testing H0 : 1 = 2 against H1: 1 2 2 2 where 1 and 2 are the variances of two populations. State the underlying assumptions. c) Define crude death rate (C.D.R.) and age specific death rate (A.S.D.R.). Find the C.D.R. in terms of A.S.D.R. Also state one application of C.D.R. Q3) Attempt any two of the following: [5 ] a) Explain the term sampling distribution of a statistic. Also obtain the sampling distribution of sample mean of a r.s. of size n drawn from exponential distribution with parameter . b) Let X follows t-distribution with n d. f. Find (2r)th central moment of X. c) In a departmental examination, the result of candidates of both the genders is as presented in following table: Gender Fail Male 40 60 Female [3717]-214 Pass 70 60 -2- Do the data support the claim that the result of the test is associated with gender of the candidate? (Use 5% level of significance.) Q4) Attempt any one of the following : a) i) Explain the small sample test for testing H0 : = 0 against H1 : 0, when 2 is unknown. Also state 100 (1 )% confidence interval for population mean ( ) when 2 is unknown. [7] ii) b) if X1 and X2 are independent and identically distributed N(4 ,1) variates , find P( 0.296 < (X1 X2)2 < 0.910). [3] i) If X Fn , n and Y Fn , n then show that 12 21 1 P (X a ) + P Y = 1. Also, if X F3,6 and Y F6,3 , find the a value of P (X 10 )+ P (Y 0.1). ii) [5] Compute total fertility rate for the following data: [5] Age group Number of women Number of births 15- 20 24,000 800 20-25 20,000 2400 25-30 15,000 2000 30-35 12,000 600 35-40 6.000 120 40-45 4,000 10 ]]]] [3717]-214 -3-

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Additional Info : S.Y. B.Sc. Statistics (Semister - II), ST - 222 : Continuous Probability Distributions - II & Demography (New Course), Pune University
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