GATE ES Probability and Statistics PYQs & Answers

Questions 1–10 of 14. Imported answers require independent review unless marked reviewed.

A box contains 26 cards with all English alphabets from A to Z. The probability of randomly choosing the card with either ‘E’ or ‘S’ from this box is ______.

Your answerChoose one option.

2/26

1/26

3/26

4/26

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Which ONE of the following options is the CORRECT formula for Chi-Square (

) test?

Given,

are the observed values,

are the corresponding expected values,

is the mean of observed values,

is the number of observations,

is the mean of

is the standard deviation of observed values, and

is the standard deviation of expected values

Your answerChoose one option.

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A 6-hour rainfall of 6 cm at a station was found to have a return period of 40 years. The probability that a 6-hour rainfall of this or larger magnitude will occur at least once in 20 successive years at that station is ______ (rounded off to three decimal places).

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Consider the following statements

(i) Environmental pollutant concentration is generally modeled using lognormal distribution. (ii) Environmental pollutant concentration is generally modeled using Poisson distribution. (iii) The weekly rate of exceedance of environmental pollutant concentration with regard to a given standard is generally modeled using lognormal distribution. (iv) The weekly rate of exceedance of environmental pollutant concentration with regards to a given standard is generally modeled using Poisson distribution.

Choose the correct option(s) from the following

Your answerSelect all correct options. You can choose more than one.

(i) and (iv) are correct

(i) is correct and (iii) is incorrect

(ii) and (iv) are correct

(ii) and (iv) are incorrect

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A residential family is considering two cities for relocation. The data related to pollutant exposure and associated health cost per year are given in the following figure.

Diagram for Environmental Science and Engineering question 47

The pollutant exposure is characterized in high, mild and low exposure categories with respective probability values. The difference in expected value of health cost of City 1 with respect to that of City 2 is ____________ lakhs/year. (rounded off to two decimal places).

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The probability of a boy or a girl being born is 1/2. For a family having only three children, what is the probability of having two girls and one boy?

Your answerChoose one option.

3/8

1/8

1/4

1/2

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Ten cards in a pack are numbered as 1, 2, 3, . . .10. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is ______.

Your answerChoose one option.

4/10

6/10

2/10

3/10

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A population (with mean

) follows normal distribution. Ten samples (N) are drawn at random with a mean value of “x” and standard deviation of “S”. Following table provides the confidence limits, C(t) of the cumulative probability function for Student’s t – distribution two-tailed test with degree of freedom D.

Which one of the following expression is correct for testing the null hypothesis H₀:

at 10% significance level?

D	C(t)=0.9	C(t)=0.95	C(t)=0.975
9	1.38	1.83	2.26
10	1.37	1.81	2.23
11	1.36	1.80	2.20

Your answerChoose one option.

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A researcher compiled the following information about the performance of a kit in an outbreak

Infection state | Kit response Disease (probability = 0.002) | Positive response (probability = 0.98) No Disease | Positive response (probability = 0.03)

The probability of detecting an infection for a positive result through the kit would be _____________ (rounded off to three decimal places).

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W₁, W₂, W₃...W₉ represent the holding times of 9 water samples, which follow a normal distribution with mean = 8.33 and standard deviation = 4.472. M represents the sample mean value of holding times, which also has a normal distribution. Assuming Z has a standard normal distribution (mean = 0 and standard deviation = 1), select the correct statement which describes the expression for calculating the value of type 1 error where

null hypothesis (H₀): M > 6

alternate hypothesis (Hₐ): M ≤ 6

Your answerChoose one option.

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GATE ES Probability and Statistics PYQs

How to practice Probability and Statistics

Question 14

Question 15

Question 34

Question 24

Question 47

Question 7

Question 11

Question 36

Question 30

Question 36