GATE ECE

Probability and Statistics

Engineering Mathematics

(Past Years Questions)

Marks 1

More
$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate...
GATE ECE 2017 Set 2
Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on t...
GATE ECE 2017 Set 1
The second moment of a Poisson-distributed random variables is $$2.$$ The mean of the random variable is _______.
GATE ECE 2016 Set 1
The variance of the random variable $$X$$ with probability density function $$\,f\left( x \right) = {1 \over 2}\left| x...
GATE ECE 2015 Set 3
Let the random variable $$X$$ represent the number of times a fair coin needs to be tossed till two consecutive heads ap...
GATE ECE 2015 Set 2
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is ...
GATE ECE 2015 Set 2
Suppose $$A$$ & $$B$$ are two independent events with probabilities $$P\left( A \right) \ne 0$$ and $$P\left( B \right)...
GATE ECE 2015 Set 1
Let $$X$$ be a zero mean unit variance Gaussian random variable. $$E\left[ {\left| X \right|} \right]$$ is equal to ____...
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 ...
GATE ECE 2014 Set 4
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss i...
GATE ECE 2014 Set 3
In a housing society, half of the families have a single child per family, while the remaining half have two children pe...
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 mea...
GATE ECE 2014 Set 1
Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ ...
GATE ECE 2012
A fair dice is tossed two times. The probability that the $$2$$nd toss results in a value that is higher than the first ...
GATE ECE 2011
A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?
GATE ECE 2009
If $$E$$ denotes expectation, the variance of a random variable $$X$$ is given by
GATE ECE 2007
A fair dice is rolled twice. The probability that an odd number will follow an even number is
GATE ECE 2005

Marks 2

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

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