M.Sc. (Semester (CBCS) Examination Oct/Nov-2017
Statistics
STATISTICAL COMPUTING
Day Date: Saturday, 25-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Attempt five questions
Q. No. and Q. No. are compulsory.
Attempt any three from Q. No.(3) to Q. No.(7)
Figures to the right indicate full mark
Q.1 Choose the correct alternatives: 05
Trapezoidal rule is used to
Solve an equation Maximize a function
Find numerical integration None of the above
Using Congruential random number generator, we obtain
numbers.
True Pseudo
Both None of these
The operator is used to compare two values in R.

None of these
In is used to extract data from a specified location.

Data.extract( All of the above
In to obtain inverse of matrix the command used is
inverse
inv.squar(A) None of these
Q.1 Fill in the blanks 05
To obtain CDF of Normal variate at point 0.22, we use
command in R.
In the command for matrix multiplication of A and B is
Using CLT, the minimum number of iid uniform random variates
required to obtain a single normal variate is
Negative binomial variate can be generated by adding
variates.
To obtain the absolute value of an argument, command is
used in MS Excel.
Q.1. State whether following statements are true or false 04
R-Software uses only text file (.txt) as an external file to import.
To assign a value to a variable, operator is used in R.
Jack-knife is a re-sampling technique
In the matrix data can be entered column-wise only.
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SLR-MS-642
Q.2 Explain the method of generating random numbers from bivariate
Poisson distribution.
Explain trapezoidal rule to find numerical integration.
06
Write short notes on the following
Monte-Carlo method to estimate
Bootstrap technique
08
Q.3 State and prove the result to obtain Geometric random variates using iid
variates.
07
Write an algorithm to generate 20 observations from
multinomiall(𝑛, distribution.
07
Q.4 Explain the method of obtaining random numbers from using
multiplicative congruential random numbers.
07
Explain any two methods to check uniformity of random numbers. 07
Q.5 Discuss matrix operations in R. 07
Write an R-program to compute factorial of a positive integer. 07
Q.6 Discuss Jack-knife technique. Obtain Jack-knife estimator of if X1,
X2,….,Xn) are iid
07
Explain Newton-Raphson method to obtain root of the equation 0. 07
Q.7 Explain the regula falsi method. 07
Write minitab macros to:
Generate 100 observations from Poisson distribution with mean=3
Generate 100 observations from B(10,0.5).