LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – STATISTICSTHIRD SEMESTER – NOV 2006ST 3810 – STATISTICAL COMPUTING – II
Date & Time : 30-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks
(i) Choose either 1 or 2(ii) 3 is compulsory(iii) Choose either 4 or 5(iv) 1. Compare the performances of SRS-HTE strategy and SRS-HARTELY ROSS UNBIASED RATIO TYPE ESIMATOR strategy in estimating total population during the year 2006 using the following population data assuming the sample size is 2 (Treat 2004 data as auxiliary information)
Area : 1 2 3 4
Population in 2004 : 37 36 48 51 (in ‘000)
Population in 2006 : 41 49 51 57 (in ‘000)
2. Certain characteristics associated with a few recent US presidents are listed below:
President Birth region Elected first time Party Prior congressional experience Served as vice presidentReagen Midwest Yes Republican No NoCarter South Yes Democrat No NoFord Midwest No Republican Yes YesNixon West Yes Republican Yes YesJohnson South No Democrat yes Yes Define suitable binary variables to convert the above data into categorical data. Form clusters using single and complete linkage methods with suitable similarity measure. Draw dendograms and compare your results.
3. (a) It is decided to estimate the proportion of students in a college having the habit of indulging in malpractice during examinations. Two random experiments were deviced. Device 1 when conducted will result in either the question “Do you indulge in copying during examinations ? “ or “Do you know the first prime minister of India ?” with probabilities 0.4 and 0.6 respectively. Device 2 also results in one of those two questions with probabilities 0.45 and 0.55. The following is the data collected from 2 independent SRSWRs of sizes 10 and 15. Responses from the first and second samples which used device 1and device 2 are
yes,no,yes,yes,no,no,yes,yes,no,no
and no, no, yes,yes,no,yes,yes,no,yes,no,no,no,yes,yes,no
Estimate the proportion of students in the college who got the habit of using unfair means during exams and also estimate the variance of your estimate.
(b) Given the normal distribution Np , where
= and =
(i) Find the distribution of CX, where C = (1, -1 , 1 )(ii) Find the conditional distribution of [X1, X2] X3 = 190; [ X1, X3] X2 = 160 ; X1 [ X2 = 150 , X3 = 180]
4. (a) A certain genetic model suggests that the probabilities of a particular trinomial distribution are respectively P1 = p 2, P2 = 2p(1-p) and P 3 = (1-p2) , 0 < p < 1. If x1, x2 and x3 represent the respective frequencies in n independent trials, how we would check on the adequacy of the genetic model given x1 = 25 , x2 = 35 and x3 = 40. (b) The following table gives the probabilities and the observed frequencies in 4 phenotypic classes AB, Ab, aB, ab in a genetical experiment. Estimate the parameter by the method of maximum likelihood and find the standard error.
Class : AB Ab aB ab Prabability : Frequency : 102 25 28 5 (16+17)
5. (a) A markov chain with state space has tpm given by Find (i) equivalence classes. (ii) recurrent and transient states (iii) mean recurrence time for recurrent states (iv) periodicity of the states.
(b) A Markov chain with state space Obtain the steady state distribution of the Markov chain.
Latest Govt Job & Exam Updates: