GATE XE Probability and Statistics PYQs & Answers

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

Which of the following statements is/are true?

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

and

are estimated as lines of regression of

and

, respectively.

and

are estimated as lines of regression of

and

, respectively.

and

are estimated as lines of regression of

and

, respectively.

and

are estimated as lines of regression of

and

, respectively, and the correlation between

and

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Let

be a random variable having probability density function (pdf)

Then, the value of the expectation of

(rounded off up to two decimal places) is __________

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Let

and

be two random variables with mean 0, variance 1, and correlation coefficient

. Then the value of

is equal to

Your answerChoose one option.

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There are four cities, namely,

and

. The cities are directly connected by four roads as shown in the picture given below, that is,

is connected with

, and

is connected with

. The probability of any road getting blocked is

. Let

be the event of traveling from

via

and

be the event of traveling from

via

. Then, which of the following statements is correct?

Diagram for Engineering Sciences question 13

Your answerChoose one option.

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The probability of a person telling the truth is

. An unbiased die is thrown by the same person twice and the person reports that the numbers appeared in both the throws are same. Then the probability that actually the numbers appeared in both the throws are same is __________ (round off to 2 decimal places).

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In a cosmopolitan city, the population comprises of 30% female and 70% male. Suppose that 5% of female and 30% of male in the population are foreigners. A person is selected at random from this population. Given that the selected person is a foreigner, the probability that the person is a female is ________ (round off to three decimal places).

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A person, who speaks the truth 3 out of 4 times, throws a fair dice with six faces and informs that the outcome is 5. The probability that the outcome is really 5 is ________ (round off to three decimal places).

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Let

be a random variable with probability density function

Let

. Then the probability

depends only on

Your answerChoose one option.

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Players

and

take turns to throw a fair dice with six faces. If

is the first player to throw, then the probability of

being the first one to get a six is ____ (round off to two decimal places).

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Let

be the Poisson random variable with parameter

. Then, the probability

equals

Your answerChoose one option.

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GATE XE Probability and Statistics PYQs

How to practice Probability and Statistics

Question 14

Question 17

Question 11

Question 13

Question 20

Question 17

Question 7

Question 9

Question 11

Question 1