GATE MT Probability and Statistics PYQs & Answers

Questions 1–10 of 17. Imported answers require independent review unless marked reviewed.

A box contains 20 thermometers, 3 of which are defective. One person randomly draws 2 thermometers from the box, one-by-one, without replacement. The probability in percent (rounded-off to two decimal places) that none of these TWO thermometers is defective, is _________________ %.

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Consider a distribution with the following probability density function

Given that the mean of the above probability distribution is 1, the variance (rounded off to two decimal places) is ________________.

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A linear regression model was fitted to a set of

data. The total sum of squares and sum of squares of error are 120 and 12, respectively. The coefficient of determination (

) of the fit is _____ (rounded off to one decimal place).

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and

are independent normally distributed random variables with means

and

, and variances

and

, respectively, then the combination

has mean

and variance

such that

Your answerChoose one option.

and

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Consider the normal (Gaussian) distributions

shown in the figure.

and

are the standard deviation and mean of distribution

, respectively, and the means are positive. Which one of the following deductions is correct?

Diagram for Metallurgical Engineering question 13

Your answerChoose one option.

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The probability of setting an easy exam paper by three setters are

, and

. If all three are setting one paper each, then the probability that at least one of the papers will be easy is __________ (round off to 2 decimal places).

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A set of observations with normal distribution of error as ±1.96σ (where σ is standard deviation) is equivalent to the confidence interval of _______% (round off to the nearest integer).

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A set of 11 (x, y) data points is least-squares fitted to a quadratic polynomial. If the sum of squares of error is 2.4, the variance of error is ________ (round off to 1 decimal place).

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A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ______

Your answerChoose one option.

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The grain size (X) of annealed specimens follows a symmetric distribution with a mean (μ) of 5 μm and a standard deviation (σ) of 0.5 μm. The percentage of specimens with grain size in the range 5 to 6 μm is expected to be: __________ (round off to nearest integer).

Given: For the symmetric distribution: Probability P(X ≤ μ + 2σ) = 0.98

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GATE MT Probability and Statistics PYQs

How to practice Probability and Statistics

Question 33

Question 44

Question 35

Question 11

Question 13

Question 31

Question 34

Question 64

Question 7

Question 15