Probability and Statistics · Engineering Mathematics · GATE ECE

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Marks 1

GATE ECE 2022
The bar graph shown the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler h...
GATE ECE 2018
Let X1 , X2 , X3 and X4 be independent normal random variables with zero mean and unit variance. The probability that X4 is the smallest among the fou...
GATE ECE 2017 Set 1
Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to ...
GATE ECE 2017 Set 2
$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: ...
GATE ECE 2016 Set 1
The second moment of a Poisson-distributed random variables is $$2.$$ The mean of the random variable is _______.
GATE ECE 2015 Set 2
Let the random variable $$X$$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The e...
GATE ECE 2015 Set 2
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $$1/6$$ and that of Ramesh is ...
GATE ECE 2015 Set 3
The variance of the random variable $$X$$ with probability density function $$\,f\left( x \right) = {1 \over 2}\left| x \right|{e^{ - \left| x \right...
GATE ECE 2015 Set 1
Suppose $$A$$ & $$B$$ are two independent events with probabilities $$P\left( A \right) \ne 0$$ and $$P\left( B \right) \ne 0.$$ Let $$\overrigh...
GATE ECE 2014 Set 4
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier of future calls, t...
GATE ECE 2014 Set 4
Let $$X$$ be a zero mean unit variance Gaussian random variable. $$E\left[ {\left| X \right|} \right]$$ is equal to ______
GATE ECE 2014 Set 3
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
GATE ECE 2014 Set 1
Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mean values of $$X$$ and $${{X^2}...
GATE ECE 2014 Set 1
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that...
GATE ECE 2012
Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\le...
GATE ECE 2011
A fair dice is tossed two times. The probability that the $$2$$nd toss results in a value that is higher than the first toss is
GATE ECE 2009
A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?
GATE ECE 2007
If $$E$$ denotes expectation, the variance of a random variable $$X$$ is given by
GATE ECE 2005
A fair dice is rolled twice. The probability that an odd number will follow an even number is

Marks 2

GATE ECE 2017 Set 2
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $$40$$% chance of...
GATE ECE 2016 Set 3
The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a ''head'' is obtained. If the ...
GATE ECE 2016 Set 1
Two random variables $$X$$ and $$Y$$ are distributed according to $$${f_{X,Y}}\left( {x,y} \right) = \left\{ {\matrix{ {\left( {x + y} \right),} &...
GATE ECE 2015 Set 2
Let $$\,\,X \in \left\{ {0,1} \right\}\,\,$$ and $$\,\,Y \in \left\{ {0,1} \right\}\,\,$$ be two independent binary random variables. If $$\,\,P\left(...
GATE ECE 2015 Set 3
A fair die with faces $$\left\{ {1,2,3,4,5,6} \right\}$$ is thrown repeatedly till $$'3'$$ is observed for the first time. Let $$X$$ denote the number...
GATE ECE 2015 Set 1
The input $$X$$ to the Binary Symmetric Channel (BSC) shown in the figure is $$'1'$$ with probability $$0.8.$$ The cross-over probability is $$1/7$$. ...
GATE ECE 2014 Set 4
Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a probability $${1 \over 5}$$ of losi...
GATE ECE 2014 Set 3
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ________.
GATE ECE 2014 Set 3
Let $${X_1},{X_{2,}}$$ and $${X_{3,}}$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,1} \...
GATE ECE 2014 Set 2
Let $$X$$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $$100.$$ The expectation, $$E\left[ X \right],...
GATE ECE 2014 Set 1
Let $$\,{X_1},\,\,{X_2}\,\,$$ and $$\,{X_3}\,$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ ...
GATE ECE 2013
Let $$U$$ and $$V$$ be two independent zero mean Gaussian random variables of variances $${1 \over 4}$$ and $${1 \over 9}$$ respectively. The probab...
GATE ECE 2013
Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution functions of $$U$$ and $$2V$$ be $$...
GATE ECE 2012
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
GATE ECE 2010
A fair coin is tossed independently four times. The probability of the event ''The number of times heads show up is more than the number of times tai...
GATE ECE 2009
A discrete random variable $$X$$ takes value from $$1$$ to $$5$$ with probabilities as shown in the table. A student calculates the mean of $$X$$ as $...
GATE ECE 2009
Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ w...
GATE ECE 2007
An examination consists of two papers, paper $$1$$ and paper $$2.$$ The probability of failing in paper $$1$$ is $$0.3$$ and that in paper $$2$$ is $$...
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