# Andhra University BE/B.Tech Probability Statistics and Queuing Theory Previous Paper 2007

First Question so compulsory.

Answer any FOUR from the remaining questions.

All questions carry equal marks.

Answer All parts of any question at one place.

1. (a) Define the addition and multiplication therem of probability.

(b) What is meant by mathematical expectation?

(c) List any two properties of binomial distribution.

(d) List any two properties of binomial distribution.

(e) Define N Model.

(f) Briefly describe a queue.

(g) List any two limitations of χ^{2}-tests.

2. (a) State an prove Baye’s theorem.

(b) If A and B be events with P(A)=1/2 P(B)=1/3 and P(A Intersection B)=1/4 find

(1) P(A/B) (2) P(B/A) (3) P(A Union B) (4) P(A^{c}/B^{c}).

3. (a) Derive gthe moment generationg function of a binomia distribution. Also derive the moments from the mement generating functions.

(b) In a distribution exactly normal 7% of the items are under 35 and 89% are under 63. What are the mean and standard deviations of the classifications?

4. (a) If X hasz an exponential distribution with mean 2, find P[X<1/X<2].

(b) If x follows an exponential distribution with parameter 1, find the distribution of Y=X/(1+X).

5. (a) Find the maximum likelihood estimator for random sampling from a normal population for population mena when the population variance is unknown.

(b) Find the correlation coffecient for the following data:

X: 1 2 3 4 5 6 7 8 8 10

Y: 10 12 16 28 25 36 41 49 40 50

6. (a) Two samples of θ and 5 items respectively gave the following data:

Mean of the Ist sample :40

Standard deviation of Ist :8

Mean of second sample :50

Is the diffenrence of means significant?

The value of ‘t’ for 9 degrees of freedom at 5% level is 2.26.

(b) It is a random sample of 600 cars making a right turn at a certain traffic junction 157 drove into the wrong lane. Test whether actuallty 30% of all drivers make this mistake or not at thing given junction use 0.05 level of significance.

7. (a) (1) Show that average number of units in a M/M/1 system I s equal to ρ/1-ρ.

(2) For the M/M/1 ueuning system find expected value of queue length ‘n’.

(b) The XYZ Company’s quality control depth is managed by a single cleark who takes on an average 5 minites in checking parts of each of the macghine coming for inspection. The machines arrive once in every 8 minutes on the average one hour of the machine is valued at Rs. 15 and a clerk’s time is valued at Rs. 4 per hour. What are the average houly queuning system costs associated with quality control department?

8. (a) Define the following concepts

(1) Unbiasedness

(2) Consistency

(3) Large and small samples

(4) Null hypothesis and power of the test.

(b) In an experiment of immunization of cattle from tuberculosis the following results were obtained.

Affected Not affected

Inoculated 12 26

Not-inoculated 16 6

Calculate χ ^{2 }and siscuss the effects of vacine in controlling susceptibility to tuberculosis (5% value of χ^{2} for one degee of freedom =3.84).

## Leave a Reply

You must be logged in to post a comment.