University of Pune 2010 M.C.A PROBABILITY AND COMBINATORICS (Old)(2005 Pattern) - Question Paper
IIII III III I II I II [3780] - 25
M.C.A. (Semester - II) (Mgmt. Faculty) Examination, 2010 MT 21 : PROBABILITY AND COMBINATORICS (0ld)(2005 Pattern)
Time : 3 Hours Max. Marks : 70
N.B. : 1) Question No. 1 is compulsory.
2) Attempt any 2 questions from question No. 2 to question No. 4.
3) Figures to right indicate full marks.
4) Use of Calcualtors and Statistical Tables is allowed.
1. a) What is the probability that a number selected randomly from 1 to 5000 is
divisible by 2 or 5 or 9. 6
b) Determine the discrete numeric function of generating function .
A(z) = -1-2. 6
5 _ 6z + z
c) Let A, B & C be three mutually exclusive and exhaustive events defined on sample space S. If P (A) = 2 P (B) = 3 P(C). Find P (AuB). 6
d) Obtain mean and variance of Poisson distribution. 6
e) An explosion in a factory manufacturing explosions can occur due to
i) short circuit
ii) defects in machinery
iii) negligence of workers.
The probabilities of these causes are known to 0.25, 0.4 and 0.35 resp.
The engineers feel that an explosion can occur with probabilities
i) 0.35 if there is a short circuit
ii) 0.2 if there are defects in machinery
iii) 0.4 if the workers are negligent.
Given that an explosion has occurred determine that it is due to workers negligence. 6
2. a) The life time of a certain type of battery has mean of 310 hours with a standard deviation of 32 hours. Assuming that the distribution is normal. Find
1) Proportion of batteries having life time between 225 and 360 hours.
2) The life in hours above which we will find best 15% of the batteries. 8
b) If f (x, y) = e _ (x+y)
x > 0, y > 0
= 0
O.co
is the joint p.d.f. of (X,Y) find
i) P (X < 1)
6
6
8
ii) P(X>Y)
c) Find the number of integer solutions of equation x1+x2+x3 = 30 subject to the condition 4<Xj<9, 7<x2<14, 10<x3<24.
3. a) Find Mean and variance of exponential distribution.
b) Given below is the joint p.m.f. of (X, Y)
|
\y x\ |
1 |
2 |
3 |
|
-1 |
k |
2k |
3k |
|
0 |
2k |
4k |
5k |
|
1 |
3k |
5k |
6k |
Find
i) K
ii) Marginal distribution of X and Y.
iii) Conditional distribution of X given Y = 2
( 3 Y
c) Find the coefficient of xyz 2 in x - 2y + I 6
4. a) Find expectation of sum of the outcomes when two dice are rolled. Hence find
variance. 8
b) Solve recurrence relation an + 6 a +9a = 3 for n > 1 given a0 = 0 and
a1 = 1 6
c) Define moment generating function and comulant generating function with the properties. 6
B/l/10/495
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Attachment: |
| Earning: Approval pending. |
