## Old Question Paper 2071 (2014)

Subject: Probability and Statistics

Tribhuvan University – Institute of Science and technology

Bachelor Level / First Year / First Semester / Science

Computer Science and information Technology Stat. 103

Full Marks: 60 | Pass Marks: 24 | Time: 3 hours

Candidates are required to give their answers in their own words as far as practicable. All notations have the usual meanings.

## Group A – Attempt any Two: [2 X 10 = 20]

1. Explain Brave’s Theorem. Suppose that an assembly plant receives its voltage regulators from three different suppliers, 60% from suppliers B_{1}, 20% from supplier B_{2}, and `10% from supplier B_{3}. If 95% of the voltage regulators from B_{1}, 80% of those from B_{2}, and 65% of those from B_{3} perform according to specifications, compute the probability that any one voltage regulator received by the plant will perform according to specifications. Also obtain the probability that a particular voltage regulator, which is known to perform according to specifications came from supplier B_{3}.

2. (a) Define point estimation and interval estimation. Explain the criteria that an estimator is good. Show that the sample mean is an unbiased and consistent estimator of the population mean.

(b) If x̄ = 60, S = 12, n = 50, and assuming that the population is normally distributed, set up a 95% confidence interval estimate of the population mean µ.

3. (a) Explain, for what purpose, Karl Pearson’s correlation coefficient is used in statistical analysis? State its major properties.

(b) It has been realized that the production of coal in a certain coal factory has been affected to some extent by the number of workers involved. The following table shows the production of coal and the number of workers in a certain time during which the capital equipment remained constant.

Output in tons (Y) | 21 | 21 | 20 | 18 | 17 | 17 | 14 | 13 |

No of Workers (X) | 70 | 68 | 65 | 50 | 47 | 47 | 44 | 43 |

Utilizing the above data, fit a regression line of Y on X, and also predict Y for X = 60.

## Group B. – Answer any eight questions: [8 X 5 = 40]

4. The following are the numbers of minutes that a person had to wait for the bus to work in a local bus park of Kathmandu on 15 working days: 10, 1, 13, 9, 5, 9, 2, 10, 3, 8, 6, 17, 2, 10 and 15. Compute mean, median, mode, and explain about the shape of the distribution.

5. Define classical approach of probability. Explain conditional probabilities with suitable examples.

6. Define Binomial probability distribution. If the mean of the binomial distribution is 3 and standard deviation is 2, explain, whether this information is correct or not in the case of Binomial distribution.

7. If two random variables have the joint probability density.

Find the conditional density of the first given that the second takes on the value x_{2}.

8. Service calls come to a maintenance center according to a Poisson process and on the average 2.7 calls come per minute. Find the probability that no more than 4 calls come in any period.

9. Define normal probability distribution. Explain the important properties of normal distribution.

10. Given a random variable having the normal distribution with µ = 16.2 and σ^{2} = 1.5625, find the probabilities that it will take on a value (i) greater than 16.8, (ii) less than 14.9, (iii) between 13.6 and 18.8.

11. Define Chi square distribution and its density function. Explain under which situation Chi-square test is used in data analysis?

12. An importer is offered a shipment of machine tools for Rs 140,000, and the probabilities that he will be able to sell them for Rs 180,000, Rs 170,000 and Rs 150,000 are 0.32, 0.55 and 0.13 respectively. What is the importer’s expected gross profit?

13. Write short notes on the following:

a) Properties of standard deviation

b) Principles of least square method

## 2 Comments

dear admin

please mail me a good note of probability and statistics of 1st sem.

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