M.Sc. (Semester (CBCS) Examination Nov/Dec-2018
Statistics
STATISTICAL COMPUTING
Time: 2½ Hours Max. Marks: 70
Instructions: All Questions carry equal marks.
Figures to the right indicate full marks.
Q.1 Choose the most correct alternative 14
To obtain the arithmetic mean of arguments, the command is used
in MS-Excel.
average()
amean() none of these
The R-command to obtain value of pmf of Poisson(3) distribution at point 1 is

ppois(3,1) ppois(1,3)
dpois(1,3) none of these
To obtain one sample from bivariate exponential distribution, we need to
draw exponential random numbers.
three two
twelve one
To obtain value of pmf of Binomial distribution at point the Rcommand
is
pbinom(1, 0.1) fbinom(1, 3,0.1)
dbinom(1, 0.1) None of these
If X follows distribution, then 1-X follows
U 0,1
Beta(2, None of these
CLT is useful in generating
Uniform variates Normal variates
Binomial variates Geometric variates
The distribution function of beta distribution follows distribution.
Chi-square Normal
Beta Uniform
To assign a value to a variable, operator is used in R.

Both a and b Neither a nor b
R-command for extracting second value of vector a is
a2
None of these
10) In boot-strap technique method is used for resampling.
Stratified Systematic
SRSWR SRSWOR
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11) To obtain matrix product of A and the R-command is
A*B
None of these
12) The command is used to repeat same value in R.
repeat()
replicate() all of these
13) In equality operator is given by

Neither a nor b
14) Newton-Raphson method is used to
Find roots of the equation Maximize a function
Minimize a function Optimize a function
Q.2 Answer the following. (Any four) 08
Give an R-command to enter following matrix.

13 12 49
22 15 75
11 30 38
Write R-commands to export a file from R.
State MS-Excel commands to calculate absolute value as well as
rounded value of a number.
Write MINITAB command to obtain 10 random numbers From Bernoulli
with success probability as 0.4.
Write R-command to obtain:
Distribution function of binomial at 2.3.
ii) Distribution function of Poisson(2) at 3.5.
Write notes on following. (Any two) 06
Simpsons's method
Performing t-test in MS-Excel.
COUNTIF, COUNTIFS commands in MS-Excel.
Q.3 Answer the following. (Any two) 08
Explain various R-commands for matrix operations.
Explain regula-falsi method to obtain root of a function.
Explain any two methods to check uniformity of random numbers.
Answer the following. (Any one) 06
Explain Box-Muller transformation.
Explain various R-commands related with frequencies and cross tables.
Q.4 Answer the following. (Any two) 10
Describe how to obtain Poisson random variates from iid
variates. Also write algorithm for the same.
State and prove the result to generate observations from geometric
distribution.
Write an algorithm to generate k observations from multinomial
distribution.
Answer the following. (Any one) 04
Write MINITAB macros to:
Generate 500 observations from Normal distribution.
ii) Generate 40 observation from binomial with mean 10, variance 5.
Explain the algorithm and R-program to generate random numbers from
Bernoulli distribution with parameter p.
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Q.5 Answer the following. (Any two) 14
Discuss bootstrap method of bias reduction. State clearly the assumptions, if
any.
Discuss Jack-knife technique. Obtain Jack-knife estimator of if
… are iid
Explain the Newton-Raphson method to find root of a functions.