GATE CE

Probability and Statistics

Engineering Mathematics

(Past Years Questions)

Marks 1

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A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succ...
GATE CE 2017 Set 2
The number of parameters in the univariate exponential and Gaussian distributions, respectively, are
GATE CE 2017 Set 1
The spot speeds (expressed in km/hr) observed at a road section are $$66, 62, 45, 79, 32, 51, 56, 60, 53$$ and $$49.$$ T...
GATE CE 2016 Set 2
$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right)...
GATE CE 2016 Set 2
Type $${\rm I}{\rm I}$$ error in hypothesis testing is
GATE CE 2016 Set 1
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes; (i) Head, (ii) Head, ...
GATE CE 2014 Set 2
The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200...
GATE CE 2012
Two coins are simultaneously tossed. The probability of two heads simultaneously appearing
GATE CE 2010
Three values of $$x$$ and $$y$$ are to be fitted in a straight line in the form $$y=a+bx$$ by the method of least square...
GATE CE 2008
If the standard deviation of the speed of vehicles in a highway is $$8.8$$ kmph and the mean speed of the vehicles is $$...
GATE CE 2007
A box contains $$10$$ screws, $$3$$ of which are defective. Two screws are drawn at random with replacement. The probabi...
GATE CE 2003

Marks 2

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For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which o...
GATE CE 2017 Set 1
If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$$f\left( x \right) = \left\{ {\matrix{ {{x \over a...
GATE CE 2016 Set 2
The probability density function of a random variable, $$x$$ is $$$\matrix{ {f\left( x \right) = {x \over 4}\left( {...
GATE CE 2015 Set 2
Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability ...
GATE CE 2015 Set 2
Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$$p\left( {x,q} \right) = \left\{...
GATE CE 2015 Set 1
An observer counts $$240$$veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poiss...
GATE CE 2014 Set 2
If $$\left\{ x \right\}$$ is a continuous, real valued random variable defined over the interval $$\left( { - \infty ,\,...
GATE CE 2014 Set 2
The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E ...
GATE CE 2014 Set 1
A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of ...
GATE CE 2014 Set 1
Find the value of $$\lambda $$ such that the function $$f(x)$$ is a valid probability density function ________.
GATE CE 2013
Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one neg...
GATE CE 2012
There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls a...
GATE CE 2011
The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( ...
GATE CE 2009
A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Gi...
GATE CE 2004

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