BE Computer Engineering (Pokhara University) Probability and Statistics (PU, MTH 216) Question Paper 2078
This is the official BE Computer Engineering (Pokhara University) Probability and Statistics (PU, MTH 216) question paper for 2078, as set in the regular annual examination. It carries 100 full marks and a time allowance of 180 minutes, across 12 questions. On Kekkei you can attempt this Probability and Statistics (PU, MTH 216) past paper online with a timer, get instant AI feedback and step-by-step solutions, and track the topics where you lose marks — completely free. Whether you are revising for your BE Computer Engineering (Pokhara University) Probability and Statistics (PU, MTH 216) exam or solving previous years' question papers, this 2078 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt all / any as specified.
The following data represent the time (in milliseconds) taken by a web server to respond to 40 requests during a load test:
| Response time (ms) | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 |
|---|---|---|---|---|---|---|
| Number of requests | 4 | 7 | 12 | 9 | 5 | 3 |
(a) Compute the arithmetic mean, median and mode of the response times. (6)
(b) Compute the standard deviation and the coefficient of variation, and comment on the consistency of the server's response. (5)
(c) Calculate the coefficient of skewness (Karl Pearson's) and interpret the shape of the distribution. (3)
A software company procures identical microcontroller chips from three suppliers A, B and C, which supply 50%, 30% and 20% of the total stock respectively. From past experience it is known that 2%, 3% and 4% of the chips from suppliers A, B and C respectively are defective.
(a) State Bayes' theorem and the theorem of total probability, clearly explaining the meaning of prior and posterior probability. (4)
(b) A chip is selected at random from the combined stock. Find the probability that it is defective. (4)
(c) Given that a randomly chosen chip is found to be defective, find the probability that it was supplied by supplier C. (4)
(d) Which supplier is most likely to be the source of a defective chip? Justify your answer. (2)
The following table shows the number of hours (X) eight students spent practising programming per week and their scores (Y) out of 100 in a coding assessment:
| X (hours) | 2 | 4 | 5 | 6 | 8 | 9 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|
| Y (score) | 40 | 48 | 55 | 60 | 70 | 72 | 85 | 90 |
(a) Compute the Karl Pearson coefficient of correlation between X and Y and interpret it. (5)
(b) Fit the least-squares regression line of Y on X. (5)
(c) Estimate the expected score of a student who practises 10 hours per week, and explain the meaning of the coefficient of determination for this fit. (4)
A manufacturer claims that the mean lifetime of its LED bulbs is at least 8000 hours. A quality-control engineer tests a random sample of 36 bulbs and finds a sample mean lifetime of 7820 hours with a sample standard deviation of 480 hours.
(a) Explain the difference between a Type I and a Type II error, and define the level of significance and the p-value of a test. (4)
(b) Formulate the null and alternative hypotheses and, at the 5% level of significance, test whether the manufacturer's claim is justified. (6)
(c) Construct a 95% confidence interval for the true mean lifetime of the bulbs and state whether it is consistent with your conclusion in part (b). (4)
Section B: Short Answer Questions
Attempt all / any as specified.
Two cards are drawn one after another without replacement from a well-shuffled standard deck of 52 playing cards. Find the probability that (a) both cards are aces, (b) the first is a king and the second is a queen, and (c) at least one of the two cards is a spade. State clearly any addition or multiplication rule of probability you use.
In a digital communication channel, bits are transmitted independently and each bit is received in error with probability 0.01. A packet consists of 100 bits. Using a suitable approximation, find the probability that a packet contains (a) no error and (b) at most two errors. State the distribution you used and justify why the approximation is appropriate.
The lengths of bolts produced by a machine are normally distributed with mean 50 mm and standard deviation 1.5 mm. A bolt is acceptable if its length lies between 47.5 mm and 52.5 mm. (a) What percentage of bolts produced are acceptable? (b) If 2000 bolts are produced in a shift, how many are expected to be rejected? (Use standard normal tables.)
A continuous random variable X has the probability density function
(a) Determine the value of the constant k. (b) Find the mean E(X) and the variance Var(X) of X. (c) Compute P(X > 1).
(a) Distinguish between a parameter and a statistic, and explain the terms 'sampling distribution' and 'standard error' with an example. (3)
(b) State the Central Limit Theorem and explain its significance in statistical inference for large samples. (3)
In a survey, 360 out of 600 randomly selected smartphone users said they prefer Android over iOS. Test, at the 1% level of significance, the hypothesis that 50% of all users prefer Android. State your hypotheses, the test statistic used, and your conclusion.
A die is rolled 120 times and the following frequencies of the faces are observed:
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 15 | 22 | 18 | 24 | 21 | 20 |
Using the chi-square goodness-of-fit test at the 5% level of significance, test whether the die is fair.
Write short notes on any TWO of the following: (a) Skewness and kurtosis as measures of the shape of a distribution; (b) Mathematical expectation and its properties for a discrete random variable; (c) Mutually exclusive events versus independent events, with one example of each.