TRIBHUVAN UNIVERSITY
INSTITUTE OF SCIENCE AND TECHNOLOGY
2079 B.S.
Candidates are required to give their answers in their own words as far as practicable.
Group A
Long Answer QuestionsAttempt any Two questions.
- 1What do you understand by measures of dispersion? What are the different measures of dispersions? The following table shows the data of time taken( in seconds) for completing each one of series of 80 similar chemical experiments | Time(s) | 56-60 | 61-65 | 66-70 | 71-75 | 76-80 | | :--- | :--- | :--- | :--- | :--- | :--- | | Number of experiments | 8 | 12 | 28 | 22 | 10 | Calculate mean time of experiments, standard deviation and variance and comment on your results.
- 2What are the assumptions for Pearson's correlation? Bradford Electric Illuminating is studying the relationship between kilowatt- hours (thousands) used and the number of rooms in a private single family residence. A random sample of 5 houses yields the following. | Number of rooms | 11 | 10 | 14 | 7 | 9 | | :--- | :--- | :--- | :--- | :--- | :--- | | Kilowatts-hours (thousands) used | 9 | 8 | 11 | 5 | 9 | Find the correlation coefficient between number of rooms and kilowatts-hours used. Interpret the result. Determine the regression equation of kilowatts hours used on number of rooms. Interpret the value of regression coefficient. Estimate the kilowatts-hours used for a 8 room house.
- 3Under what conditions Binomial distribution tends to Poisson distribution? The number of telephone calls receive during the month of May is summarizing in the following table. | Normal of telephone calls per day | 0 | 1 | 2 | 3 | 4 | | :--- | :--- | :--- | :--- | :--- | :--- | | Number of days | 8 | 12 | 18 | 13 | 9 | Find the Poisson distribution.
Group B
Short Answer QuestionsAttempt any Eight questions.
- 4The following table shows the marks obtained by 130 students in computer science. | Marks | Less than 40 | 40-50 | 50-60 | 60-70 | 70-80 | 80 or above | | :--- | :--- | :--- | :--- | :--- | :--- | | Numbers of students | 14 | 24 | 36 | 25 | 20 | 11 | Find the appropriate measure of central tendency. Compute the minimum marks obtained by the top 20% of students.
- 5Two batsmen A and B made the following runs in a series of cricket matches. | A | 10 | 0 | 56 | 80 | 24 | | :--- | :--- | :--- | :--- | :--- | :--- | | B | 36 | 37 | 45 | 28 | 29 | Who is more consistent players, and how?
- 6Define conditional probability. A problem of Statistics is given to three students, A, B and C whose chances of solving the problem are in ration 2:3:5. Find the probability that (i) none of them solve the problem. (ii) the problem will be solved.
- 7A factory has three machines M1, M2 and M3 producing large numbers of computer chips. Of the total daily production of the item 50% produce on M1, 20% on M2 and 30% on M3. Records show that 4% of chips production on M1 are defective, 2% of chps produced on M2 are defective and 2.5% of chips production on M3 are defective. The occurrence of defective chips is independent of all other chips. One chips is chosen at random from a day's total production (i) show that the probability of its being defective is 0.0315 (ii) Given that is defective, find the probability that it was produced on machine M1.
- 8A coin is tossed for two times and if X denotes the number of heads obtained find (i) $E(X)$ (ii) $E(X^2)$ (iii) $V(X)$ (iv) $E(2X^2+3X-5)$
- 9The mean and variance of number of flights arriving late in a day are 2 and 1.6 respectively. Assuming binomial distribution, are these values consistent? If yes, find the probability that (i) none of the flights are late today (ii) at least one flight late today.
- 10What do you understand by normal distribution? From a batch of 10000, the life time on laptop batteries have normal distribution with mean 40 months and standard deviation 8 months. What is the probability that a laptop selected at random will have life time (i) more than 50 months? (ii) Between 40 and 50 months?
- 11If X and Y are two random variables having joint density function: $f(x,y)=\frac{1}{8}(6-x-y)$, $0<x<2, 2<y<4$ $=0$, otherwise. find $P(X<1.5 \text{ and } 1<Y<3)$
- 12What do you understand by sampling? Differentiate between simple random sampling and stratified random sampling.
- 13Write short note on any two: (i) Normal and ordinal scale (ii) Kurtosis (iii) Five number Summary.