GATE MN topic:probability-and-statistics PYQs & Answers

Questions 1–10 of 26. Imported answers require independent review unless marked reviewed.

Match the distribution with its corresponding probability density/mass function.

Distribution type	Probability density/mass function
(P) Binomial Distribution	(1)
(Q) Poisson Distribution	(2)
(R) Normal distribution	(3)
(S) Exponential Distribution	(4)

Your answerChoose one option.

P → 2, Q → 3, R → 1, S → 4

P → 1, Q → 3, R → 2, S → 4

P → 3, Q → 2, R → 1, S → 4

P → 2, Q → 4, R → 3, S → 1

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Using linear regression (least squares), the best-fit line for the given dataset is y = 2.2x + 2.3. Given the residual sum of squares is 25.8, the coefficient of determination (

), is _____________. (rounded off to two decimal places)

x	2	3	4	5
y	8	9	7	16

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A thermal power plant has an agreement with three mines M1, M2 and M3 to receive ‘Grade 1’ coal, in the proportion of 60%, 25% and 15%, respectively. The probabilities that a wagon supplied coal to the plant containing below ‘Grade 1’ from mines M1, M2 and M3 are 0.02, 0.03 and 0.04, respectively. On a random check, a sample wagon is found to carry below ‘Grade 1’ coal. The probability that the wagon belongs to mine M1, is _____. (round off up to 2 decimals)

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Given two random variables X and Y, the expected value E(3X−5Y) is

Your answerChoose one option.

3E(X) − 5E(Y)

3E(X)+5E(Y)

3E(X) − 5E(Y) − 15E(XY)

E(X) − E(Y) − E(XY)

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A regression line is constructed between shovel production rate and shovel swing angle for 50 observations as shown below.

	Estimated parameter	Standard error
Intercept	29.6	13.45
Slope	2.5	1.32

t-values corresponding to level of significance (P) and degree of freedom (DF)

DF	one-tail 0.1	0.05	0.025	0.01	0.005	0.001	0.0005
30	1.31	1.697	2.042	2.457	2.75	3.385	3.646
60	1.296	1.671	2	2.39	2.66	3.232	3.46

If residuals are normally distributed and significance tests of the parameters are conducted at 0.05 significance level, the true statement is ____

Your answerChoose one option.

Both intercept and slope are significant.

Intercept is significant but slope is not significant.

Intercept is not significant but slope is significant.

Both intercept and slope are not significant.

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The closest match of the scatter plot between the variables X and Y with the approximate attribute is

Diagram for Mining Engineering question 37

Your answerChoose one option.

P→I, Q→II, R→II, S→IV

P→II, Q→I, R→IV, S→II

P→II, Q→IV, R→I, S→II

P→IV, Q→II, R→III, S→I

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In a health centre, the probability of ‘full occupancy’ of COVID beds for a day is 0.8. Assuming Binomial probability distribution, the probability of full occupancy exactly for 5 days in a week, is ______. (round off to three decimal places)

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Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

Your answerChoose one option.

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The measures of dispersion of a dataset are

Your answerChoose one option.

standard deviation, range and mode.

standard deviation, range and interquartile range.

variance, range and median.

interquartile range, median and mode.

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The standard normal distribution is a

Your answerChoose one option.

non-parametric distribution.

single parameter distribution.

two-parameter distribution.

three-parameter distribution.

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GATE MN topic:probability-and-statistics PYQs

How to practice topic:probability-and-statistics

Question 15

Question 48

Question 45

Question 16

Question 42

Question 37

Question 44

Question 3

Question 6

Question 13