Andhra University 2005 M.C.A PROBABILITY, STATISTICS & QUEUEING THEORY - Question Paper

2005 Andhra University M.C.A Computer Applications PROBABILITY, STATISTICS & QUEUEING THEORY ques. paper

2004-05 MODEL PAPER

MCA 1.1.4 PROBABILITY, STATISTICS & QUEUEING THEORY

First ques. is Compulsory

ans any 4 from the remaining

ans all parts of any ques. at 1 place.

Time: three Hrs.
Max. Marks: 100

a) State the axioms of probability.
b) discuss confident intervals in estimation.
c) discuss the method of lowest squares.
d) discuss Principle of lowest square.
e) discuss kind I and II errors.

2. a) State and prove Baye's formula on conditional probability.

b) We are provided 3 urns as follows:
Urn A contains three red and five white marbles
Urn B contains two red and one white marble
Urn C contains two red and two white marbles.
An urn is opted at random and a marble is drawn from the urn. If the Marble is red, what is the probability that it came from urn A?

3. a) describe mathematical expectation of a random variable. Show that the expectations of the sum of 2 random variables is equal to the sum of their expectations.
b) Suppose that a pair of dice are tossed and let the random variable X denote the sum of the points. obtain the expectation of X.

4. a) describe the mean to failure of a component. For aq series systems show that 0 = E(X) = min [E(Xc)].
b) Derive Markov inequality. Hence or otherwise state and prove Chebychev inequality.

5. a) obtain the moment generating function about origin of the normal distribution.
b) Prove that a linear combination of normal variate is also a normal variate.

6. a) Derive normal equations to fit y = a + bx by the method of lowest squares.
b) Fit a lowest squares parabola having the form y = a + bx + cx-2 to the subsequent data:


X: 1.2 1.8 3.1 4.9 5.7 7.1 8.6 9.8
Y: 4.5 5.9 7.0 7.8 7.2 6.8 4.5 2.7
7. a) Show that the correlation coefficient lies ranging from x and y -1 and +1
b) compute the correlation coefficient ranging from x and y for the subsequent data.


X: 65 66 67 67 68 69 70 72
Y: 67 68 65 68 72 72 69 71
8. Arrivals at a telephone booth are considered to be Poisson with an avg. time of 12 min. ranging from 1 arrival and the next. The length of a phone call is presumed to be distributed exponentially with mean four min.

a) obtain the avg. number of persons waiting in the system.
b) What is the probability that a person arriving at the booth will have to wait in the queue?
c) What is the probability that it will take him more than 10 mm. altogether to wait for the phone and complete his call?
d) Estimates the fraction of the day when the phone will be in use.
e) The telephone department will install a 2nd booth, when convinced that an arrival has to wait on the avg. for at lowest three min. for phone. By how much the flow of arrivals should increase in order to justify a 2nd booth?

Earning:   Approval pending.