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## Marks 1

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Let X1 , X2 , X3 and X4 be independent normal random variables with zero mean and unit variance. The probability that X4...
GATE ECE 2018
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
$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate...
GATE ECE 2017 Set 2
The second moment of a Poisson-distributed random variables is $$2.$$ The mean of the random variable is _______.
GATE ECE 2016 Set 1
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
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$$represent the number of times a fair coin needs to be tossed till two consecutive heads ap... GATE ECE 2015 Set 2 Suppose$$A$$&amp;$$B$$are two independent events with probabilities$$P\left( A \right) \ne 0$$and$$P\left( B \ri...
GATE ECE 2015 Set 1
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
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
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

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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$$pass sequentially through two post - offices. Each post - office has a proba... GATE ECE 2014 Set 4 Let$${X_1},{X_{2,}}$$and$${X_{3,}}$$be independent and identically distributed random variables with the uniform di... GATE ECE 2014 Set 3 A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ... GATE ECE 2014 Set 3 Let$$X$$be a random variable which is uniformly chosen from the set of positive odd numbers less than$$100.$$The exp... GATE ECE 2014 Set 2 Let$$\,{X_1},\,\,{X_2}\,\,$$and$$\,{X_3}\,$$be independent and identically distributed random variables with the uni... GATE ECE 2014 Set 1 Consider two identically distributed zero - mean random variables$$U$$and$$V.$$Let the cumulative distribution funct... GATE ECE 2013 Let$$U$$and$$V$$be two independent zero mean Gaussian random variables of variances$${1 \over 4}$$and$${1 \over...
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
A discrete random variable $$X$$ takes value from $$1$$ to $$5$$ with probabilities as shown in the table. A student cal...
GATE ECE 2009
Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ ta...
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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