LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

M.Sc., DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2003

ST-3803/S918 – COMPUTATIONAL STATISTICS – III

10.11.2003                                                                                                           Max:100 marks

1.00 – 4.00

SECTION-A

Answer any THREE  questions.                                                                     

 

1. a) Solve the following L.P.P using SIMPLEX METHOD

MAXIMIZE         Z = 12 X₁ + 15X₂ +14 X₃

subject to                     X₁ + X₂ + X₃  100

-0.01 X₂ + 0.02 X₃  0

-0.01 X₁ + 0.01 X₂  0

X₁, X₂,      X₃   0

1. b) Solve the following game using graphical method:

 

Player -B

B₁    B₂

Player-A

(18+15.5)

2. a) Construct a network based on the following data:

ACTIVITY:                       A         B         C         D         E          F          G

t­_{o      :}                              3          2          2          2         1         4          1

t_m    :                      6          5          4          3         3         6          5

t_{P      :}                             9          8          6          10        11        8         15

PREDECESSOR:               –           –           A         B         B        C,D       E

 

 

Calculate

• The expected time and SD for each activity
• The CRITICAL PATH
• The probability that the project will be completed by 18 weeks.

1. b) Consider the inventory problem with 3 items (n = 3), the parameters of the problem are

shown below

Item                 K_I                    b_I                            h_I                     a

1                      $10                  2 units             $ 0.3                1 sq.ft

2                      $5                    4 units             $ 0.1                1 sq.ft

3                      $15                  4 units             $ 0.2                1 sq.ft

 

Assume that the total available storage space area A= 25 Sq.feet.   Determine the

optimal order quantity for the three items.

 

(20+13.5)

 

 

 

2. a) The following correlation were obtained among the responses auditory reaction times,

audiometric hearing loss,  WAIS comprehension and WAIS digital symbol for a

sample of   N = 47 males

 

• determine the partial correlation of reaction time and hearing loss with the two WAIS subset scores held constant. Test the hypothesis of zero partial correlation at 5% level.
• Compute the multiple correlation of reaction time with the other three variates. Test the hypothesis of independence of the first response and the last three.

(20)

1. b) Let X ~ N  with the mean vector .  What is the

conditional distribution of X₂  (X₁ = 8, X₃ = 5).                                                         (13.5)

 

1     2    3    4

4. a) Consider a Markov chain with TPM

• Examine whether the Markov chain is irreducible.
• Also check whether the state 4 is ergodic
• Find the stationary distribution (3.5+4+6)

1. b) Let A = B =   =    and

to be distributed independently according to trivariate normal population with

respective parameters.

 

 

 

What are the distribution of the following linear transformation of those variates.

 

(i) AX              (ii)        BX                  (iii) (X’ A   Y’ B’)        (iv) (X’ A’   X’ B’)

 

(4×5=20marks)

 

 

 

 

 

5. a) Consider a Markov chain {x_n, n }with the state space S = {0 , 1, 2, 3, 4, 5} and one

step TPM given by

 

P  =

Find the equivalence classes and the periodicity of the states.

 

1. b) For a Morkov chain with one step TPM 0        1       2

 

Find if the states are transient or recurrent.

 

 

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