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GATE PI

Probability and Statistics

Engineering Mathematics

Previous Years Questions

Marks 1

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A fair coin is tossed $$N$$ times. The probability that head does not turn up in any of the tosses is
GATE PI 2016
In a given day in the rainy season, it may rain$$70$$% of the time . If it rains, chance that a village fair will make a...
GATE PI 2014
For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean...
GATE PI 2008
The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 +...
GATE PI 2007
The life of a bulb (in hours) is a random variable with an exponential distribution $$\,\,f\left( t \right) = \alpha {e^...
GATE PI 2005
Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds $$8$$ is
GATE PI 2005

Marks 2

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A normal random variable $$X$$ has the following probability density function $$${f_x}\left( x \right) = {1 \over {\sqr...
GATE PI 2016
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event...
GATE PI 2015
A product is an assemble of $$5$$ different components. The product can be sequentially assembled in two possible ways. ...
GATE PI 2015
Marks obtained by $$100$$ students in an examination are given in the table What would be the mean, median, and mode ...
GATE PI 2014
A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard devi...
GATE PI 2014
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $...
GATE PI 2012
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, ...
GATE PI 2012
It is estimated that the average number of events during a year is three. What is the probability of occurrence of not m...
GATE PI 2011
Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin ha...
GATE PI 2010
If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that ...
GATE PI 2010
In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game ...
GATE PI 2008
Two cards are drawn at random in succession with replacement from a deck of $$52$$ well shuffled cards Probability of ge...
GATE PI 2007
If $$X$$ is a continuous random variable whose probability density function is given by $$$\,\,\,f\left( x \right) = \l...
GATE PI 2007

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