BALOCHISTAN PUBLIC SERVICE COMMISSION
COMPETITIVE EXAMINATION 2021
FOR RECRUITMENT TO THE POSTS OF
ASSISTANT COMMISSIONER/SECTION OFFICER (B-17)
IN THE SERVICES & GENERAL ADMINISTRATION DEPARTMENT
STATISTICS
Total Marks: 150 July 19, 2021 Time Allowed: 03 Hours
NOTE: i Attempt any five questions. All questions carry equal marks i.e. 30×5=150. Calculator may be allowed.
ii All the parts (if any) of each Question must be attempted at one place instead of at different places.
iii Candidate must write Q. No. in the Answer Book in accordance with Q. No. in the Q. Paper.
iv No Page/Space be left blank between the answers. All the blank pages of the Answer Book must be crossed.
v Extra attempt of any question or any part of the attempted question will not be considered.
Q No. 1 a) i Explain the importance of regression analysis. (15)
ii Segregate the 2 terms: Correlation & Regression.
iii Briefly explain the coefficient of determination (R²).
b) Discuss the significance of the assumptions underlying the method of Least Square? What is the effect, if these assumptions are violated? (15)
Q No. 2 a) Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as: (15)
| f(x, y) | x | ||
|---|---|---|---|
| 1 | 2 | 3 | |
| 1 | 0.05 | 0.05 | 0.10 |
| 2 | 0.05 | 0.10 | 0.35 |
| 3 | 0.10 | 0.15 | 0.05 |
i Evaluate the marginal distribution of X.
ii Evaluate the marginal distribution of Y.
iii Find P(Y = 3 | X = 1).
b) Elaborate the theory of Continuity Correction and Finite population Correction Factor (FPC). When are these applied? What happens if these are dropped from the formulae where their uses are recommended? (15)
Q No. 3 a) Prove that the Mean and Standard deviation of Exponential distribution are equal using the pdf: f(x) = μe^(-μx), x > 0. (15)
b) Suppose that a system contains a certain type of component whose time, in years, to failure is given by T. The random variable T is modeled nicely by the exponential distribution with mean time to failure θ = 5. If 5 of these components are installed in different systems, what is the probability that at least 2 are still functioning at the end of 8 years? (15)
Q No. 4 a) A multiple-choice quiz has 200 questions, each with 4 possible answers of which only 1 is correct. What is the probability that sheer guesswork yields from 25 to 30 correct answers for the 80 of the 200 problems about which the student has no knowledge? (15)
b) Is there any importance of Sampling in real life? Discuss its major advantages in every daily life. (15)
Q No 5 a) One-sixth of the male freshmen entering a large state school are out-of-state students. If the students are assigned at random to dormitories, 180 to a building, what is the probability that in a given dormitory at least one-fifth of the students are from out of state? (15)
b) A certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms. Assuming that the resistance follows a normal distribution and can be measured to any degree of accuracy, what percentage of resistors will have a resistance exceeding 43 ohms? (15)
Q No 6 a) Show that S² is an unbiased estimator of the parameter σ². (15)
b) The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be 2.6 grams per milliliter. Find the 95% and 99% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3 gram per milliliter. (15)
Q No 7 a) Describe Statistics. Discuss its significance in real world by giving real life examples. (15)
b) Define and contrast the 4 measurement scales (Ratio, Interval, Ordinal, and Nominal) with few real-life examples. Which scale to be used in which situation? (15)
Q No 8 a) Briefly discuss the concept of R². Why Adjusted R² is preferred over R²? Discuss in detail whether Adjusted R² be negative? (15)
b) What is experimental design? Discuss its various types with application under certain conditions. (15)
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