Tribhuvan University | Old Is Gold
Institute Of Science And Technology
Computer Science and Information Technology
Course: Probability and Statistics
Level: Bachelor | First Year | Semester: First | Year 2070 | Science
Full Marks: 60 | Pass Marks: 24 | Time: 3 Hrs
| Download - File Size: 104 kb | Question Paper Of 'Probability and Statistics' 2070 | CSIT | TU
Candidates are required to give their answers in their own words as far as practicable.
All notations have the usual meanings.
Institute Of Science And Technology
Computer Science and Information Technology
Course: Probability and Statistics
Level: Bachelor | First Year | Semester: First | Year 2070 | Science
Full Marks: 60 | Pass Marks: 24 | Time: 3 Hrs
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 with suitable examples the term 'dispersion'. State the relative and absolute measures of 'dispersion'. Describe merits and demerits of standard deviation. A merital arithmetic test for 8 questions given to a class of 32 pupils. The result were summarized in the following table.
Find the mean, median and mode of the number of correct answers. Describe the shape of the distribution.
2. Define independent and mutually exclusive events. Can two events be mutually exclusive and independent simultaneously? Support your answer with an example.
A factory has three machines A, B, C producing large number of a certain item if the daily production of the item 50% are produced on A, 30% on B and 20% on C. Record show that 2% of the item produced on A are defective, 3% of items produced on B are defective and 4% of items produced on C are defective. The occurrence of a defective item is independent of all other items.
One item is chosen at random from a day's total output.
a. Show that the probability of it being defective item is 0.027.
b. Given that it is defective, find the probability that is was produced on machine A.
3. Distinguish between correlation and Regression. Also point out the properties of regression coefficients. The following sample observation were randomly selected.
Determine the coefficient of correlation and coefficient of determination. Interpret the association between X and Y. Find the regression equation of Y on X.
Group B
Answer any eight questions: (8 x 5 = 40)
4. The continuous random variable X has the probability density function given by
Where K is constant
a) Find the value of K b) Find P(0.3 ≤ x ≤ 0.6)
5. The marks of 500 candidates in an examination are normally distributed with a mean of 45 marks and standard deviation of 20 marks.
a) Give the pass marks 40, estimate the number of candidates who passed the examination.
b) If 5% of the candidate obtain a distinction by scoring x marks or more, estimate the value of x.
6. The joint density function of w and z is given by
Find b and marginal density function.
7. Mr X recorded number of e-mails be received over of 150 days with the following results.
a) Find the mean number of e-mails per day.
b) Calculate the frequencies of the passion distribution having the some mean.
8. Distinguish between the point estimation and interval estimation. Explain how an interval estimation is better than a point estimate.
9. Explain the concept of standard error. Discuss the role of standard error in large sample theory.
10. The random variable X has the probability distribution shown below
a) Find E(x) and V(x). b) Calculate E(Y) if Y = 3X + 2.
11. The mean life of a sample of 400 fluorescent light bulbs produces by a company is found to be 1570 hours with standard deviation of 150 hour. Test the hypothesis that the mean life time of the bulbs produced by the company is 1600 hrs. against the alternative hypothesis that it is greatly than 1600 of 5% level of significance.
12. Define binomial distribution. Is there any inconsistency in the statement that the mean of binomial distribution is 20 and standard deviation is 4. If no inconsistency is found what is the value of p, q and n.
13. Find the skewness of the following set of pertaining to kilowatt hours of electricity consumed by 100 persons in a city.
Also interpret the result.
Attempt any two: (2 x 10 = 20)
1. Explain with suitable examples the term 'dispersion'. State the relative and absolute measures of 'dispersion'. Describe merits and demerits of standard deviation. A merital arithmetic test for 8 questions given to a class of 32 pupils. The result were summarized in the following table.
Find the mean, median and mode of the number of correct answers. Describe the shape of the distribution.
2. Define independent and mutually exclusive events. Can two events be mutually exclusive and independent simultaneously? Support your answer with an example.
A factory has three machines A, B, C producing large number of a certain item if the daily production of the item 50% are produced on A, 30% on B and 20% on C. Record show that 2% of the item produced on A are defective, 3% of items produced on B are defective and 4% of items produced on C are defective. The occurrence of a defective item is independent of all other items.
One item is chosen at random from a day's total output.
a. Show that the probability of it being defective item is 0.027.
b. Given that it is defective, find the probability that is was produced on machine A.
3. Distinguish between correlation and Regression. Also point out the properties of regression coefficients. The following sample observation were randomly selected.
Determine the coefficient of correlation and coefficient of determination. Interpret the association between X and Y. Find the regression equation of Y on X.
Group B
Answer any eight questions: (8 x 5 = 40)
4. The continuous random variable X has the probability density function given by
Where K is constant
a) Find the value of K b) Find P(0.3 ≤ x ≤ 0.6)
5. The marks of 500 candidates in an examination are normally distributed with a mean of 45 marks and standard deviation of 20 marks.
a) Give the pass marks 40, estimate the number of candidates who passed the examination.
b) If 5% of the candidate obtain a distinction by scoring x marks or more, estimate the value of x.
6. The joint density function of w and z is given by
Find b and marginal density function.
7. Mr X recorded number of e-mails be received over of 150 days with the following results.
a) Find the mean number of e-mails per day.
b) Calculate the frequencies of the passion distribution having the some mean.
8. Distinguish between the point estimation and interval estimation. Explain how an interval estimation is better than a point estimate.
9. Explain the concept of standard error. Discuss the role of standard error in large sample theory.
10. The random variable X has the probability distribution shown below
a) Find E(x) and V(x). b) Calculate E(Y) if Y = 3X + 2.
11. The mean life of a sample of 400 fluorescent light bulbs produces by a company is found to be 1570 hours with standard deviation of 150 hour. Test the hypothesis that the mean life time of the bulbs produced by the company is 1600 hrs. against the alternative hypothesis that it is greatly than 1600 of 5% level of significance.
12. Define binomial distribution. Is there any inconsistency in the statement that the mean of binomial distribution is 20 and standard deviation is 4. If no inconsistency is found what is the value of p, q and n.
13. Find the skewness of the following set of pertaining to kilowatt hours of electricity consumed by 100 persons in a city.
Also interpret the result.
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