Question 1
(a)
Define independent events and provide an example
3 Marks
(b)
A coin is tossed three times. What is the probability of getting exactly two heads?
4 Marks
(c)
Find the best fitting parabola:
x 1 2 3 4 5 y 2 5 10 17 26
7 Marks
Gujarat Technological UniversitySummer 2025 Examination
GTU 3130006 Probability and Statistics (PS) Summer 2025 Paper Solution & PDF
B.E. · Computer Engineering · Semester 3 · Subject Code: 3130006
Total Marks70 MarksExternal theory exam
Passing Marks23 Marks33% minimum cutoff
Exam Duration2.5 Hours2:30 PM – 5:00 PM
Paper Structure5 QuestionsWith internal OR choices
Question 2
(a)
Does there exists a binomial distribution for which variance is greater than mean?
3 Marks
(b)
A biased coin returns head 10% of times. Find the probability of getting exactly 2 heads in 10 trials using binomial distribution.
4 Marks
(c)
A factory has three machines A, B, and C producing 20%, 30%, and 50% of the total items, respectively. The probabilities of producing a defective item are 1%, 2%, and 3% for A, B, and C, respectively. If an item is defective, what is the probability that it was produced by machine B?
7 Marks
OR OPTION
(c)
A factory produces light-bulbs. The probability of a bulb being defective is 0.02. If 200 bulbs are tested, use the Poisson approximation to find the probability that at least three bulbs are defective.
7 Marks
Question 3
(a)
Find the mean and median of 2, 3, 5,
3 Marks
(b)
Calculate the rank correlation:
x 1 2 3 4 5 y 2 1 5 4
4 Marks
(c)
Find the correlation coefficient.
x 1 2 3 4 5 6 7 y
7 Marks
OR OPTION
(a)
Find mode x 0-10 10-20 20-30 30-40 y 10 20 40 30
3 Marks
(b)
Calculate first four central moments of observations 3,5,7,13
4 Marks
(c)
Find regression line of Y on X x 2 4 6 8 10 y 5 12 19 26 33
7 Marks
Question 4
(a)
Explain the terms one-tailed and two-tailed test
3 Marks
(b)
In a sample of 500 bulbs 20 are found defective. The company claims that only 2% bulbs are defective. Test the reality of claim at 5% level of significance.
4 Marks
(c)
Test whether the following samples could have been drawn from population with same SD. Sample A Sample B Size 100 200 SD
7 Marks
OR OPTION
(a)
Explain the terms null and alternate hypothesis
3 Marks
(b)
A coin returned 531 heads in 1000 tosses. Is it biased? [Use 𝛼 = 0.05]
4 Marks
(c)
Use chi-square test to determine whether smoking and hypertension are independent at 5% level of significance[𝜒2(𝛼 = 0.05, 𝑑𝑓 = 1) =
384] Smoking No Smoking Hypertension 30 20 No Hypertension 10 40
7 Marks
Question 5
(a)
State Chebyshev’s inequality.
3 Marks
(b)
Two cards are chosen randomly from deck. What is probability that (a) both are ace? (b) both are black? (c) none is ace (d) none is black
4 Marks
(c)
Weight of 1000 experimental animals is normally distributed with mean 235 grams and standard deviation 35. How many animals weigh (a) below 172 grams (b) above 312 grams (c) between 172 to 312 grams. [P(Z=1.8)=0.4641,P(Z=2.2)=0.4841]
7 Marks
OR OPTION
(a)
If A and B are independent events with P(A)=0.5, P(B)=0.4 then find P(AᴜB)
3 Marks
(b)
Find the best fitting line to the points (1,1), (2,4), (3,9), (4,16)
4 Marks
(c)
Fit the curve 𝑦 = 𝑎𝑏𝑥 x 1 2 3 4 y 35 70 140 280
7 Marks
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About this Examination Paper & Attribution
Official Gujarat Technological University (GTU) examination paper and step-by-step solutions for Probability and Statistics (PS) (Summer 2025, B.E. · Computer Engineering, Sem 3). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.