AAOCC111 Probability & Statistics Question Paper : bits-pilani.ac.in

Name of the University : Birla Institute of Technology and Science, Pilani
Subject Code/Name : AAOC C111/Probability and Statistics
Sem : II
Website : bits-pilani.ac.in
Document Type : Old Question Paper

Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/7836-AAOC_C111_515_C_2009_2.doc

Bits Pilani Probability & Statistics Questions Paper

Birla Institute of Technology and Science, Pilani
IInd Semester 2009-10 :
Comprehensive Examination (Closed Book)

Related : LBS Centre for Science & Technology State Eligibility Test Statistics Question Paper 2017 : www.pdfquestion.in/13449.html

AAOC C111 (Probability and Statistics) :

Part A

Date: 07-05-2010 (Friday)
Max. Marks: 90
Max. Time: 150 mins

Note: Attempt Part B and Part C in the separate answer sheets provided. All subparts of a question should be attempted together. The answers should be precise and up to the point. Use usual notation and symbols as and when required. All the necessary data are provided at the end of the question paper. Define the events and random variables as and when necessary.

Part B

1. (a) A construction company employs 2 sales engineers. Engineer 1 does the work in estimating cost for 70% of jobs bid by the company. Engineer 2 does the work for 30% of jobs bid by the company. It is known that the error rate for engineer 1 is such that 0.02 is the probability of an error when he does the work, whereas the probability of an error in the work of engineer 2 is 0.04. Suppose a bid arrives and a serious error occurs in estimating cost. Decide which engineer most likely submitted the bid based on respective probabilities. Justify your answer. [8]
(b) Suppose that, on average, 1 person in 1000 makes a numerical error in preparing his or her income tax return. If 10,000 forms are selected at random and examined, find the probability that at most 2 of the forms contain an error. [7]

2. (a) Let be a gamma random variable with parameters . Then using definition, find and hence find [4+4+1]
(b) A chemical reaction is run in which the usual yield is . A new process has been devised that should improve the yield. Proponents of new process claim that it produces a better yield than the old one more than of time. The new process is tested times. Let denote the number of trials in which yield exceeds and be the probability of an increased yield.
(i) Which distribution does follow?
(ii) Let the claim be accepted if . What is the probability that claim is accepted if is really only ? (use normal approximation). [2+4]

3. (a) Let and be independent binomial random variables with means 4 and 2 and variances and , respectively. If , then find moment generating function for . Does follow binomial distribution? Justify your answer. [7]
(b) Metal conduits or hollow pipes are used in electrical wiring. In testing 1-inch pipes, these data are obtained on the outside diameter (in inches) of the pipe: 1.21, 1.19, 1.20, 1.22, 1.18, 1.23, 1.17, 1.09. Assume that sampling is from normal distribution with mean and variance .
i. Find unbiased estimates for and .
ii. Find 95% confidence interval on the mean outside diameter of pipes of this type. [8]

Part C

4. The joint density function for continuous random variable (X, Y) is given by

(b). Find marginal densities for X and Y respectively. Are X and Y independent random variables? Justify your answer.

5. (a) For a given data set
x 5 15 25 35 45 50
y 10 18 20 25 32 45
i. Find the value of , and
ii. Write the normal equations and estimate the equation of line of regression of Y on x.
iii. Find the value of sample correlation coefficient for the above data. [3+4+3]

(b) Sachin Tendulkar scores runs in T-20 league match with following discrete probability density function.
Runs (X) 50 35 25 15 45 10
f(x) 0.10 0.18 0.20 0.25 0.12 0.15
Simulate the score of Sachin Tendulkar for four league matches using following three digit random numbers 976, 009, 280, and 850. Hence estimate his average score. [5]

6. A low-noise transistor for use in computing products is being developed. It is claimed that the mean noise level will be below the 3.00 dB level of products currently in use. (Assume that noise level is normally distributed).
i. Set up the appropriate null and alternative hypotheses for verifying the claim.
ii. Find the critical point for 99% confidence test based on a sample of size 20. Using the values 2.2 and 0.88 of sample mean and sample standard deviation, respectively, to test null hypothesis against alternative hypothesis defined in (i) at ? = 0.01. Justify. [7]

7. (a) A market research study is to be conducted among users of a particular type of computer system. How many users should be sampled to estimate the percentage of users who plan to add terminals to within 5 percentage points with 97% confidence?
(b) A new computer network is being designed. The makers claim that it is not compatible with 96% of the equipment already in use.
i. Set up the appropriate null and alternative hypotheses needed to support this claim.
ii. A sample of 400 equipments is tested, and 390 of these equipments require changes. That is, they are not compatible with the new network. Can H0 be rejected at 98% confidence? Justify. [3+5]

DATA PROVIDED:
P(Z<= 0.35) = 0.6368, P(Z<= 0.93) = 0.8238, P(Z<= 1.12) = 0.8686, P(Z<= 1.88) = 0.9699, P(Z<= 1.89) = 0.9706, P(Z<= 2.17) = 0.9850, P(Z<= 2.18) = 0.9854, P(Z<= 2.32) = 0.9898, P(Z<= 2.33) = 0.9901,