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GATE PI
Probability and Statistics
Engineering Mathematics
Previous Years Questions
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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
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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
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For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean...
GATE PI 2008
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The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 +...
GATE PI 2007
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The life of a bulb (in hours) is a random variable with an exponential distribution $$\,\,f\left( t \right) = \alpha {e^...
GATE PI 2005
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Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds $$8$$ is
GATE PI 2005
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Marks 2
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A normal random variable $$X$$ has the following probability density function $$${f_x}\left( x \right) = {1 \over {\sqr...
GATE PI 2016
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A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event...
GATE PI 2015
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A product is an assemble of $$5$$ different components. The product can be sequentially assembled in two possible ways. ...
GATE PI 2015
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Marks obtained by $$100$$ students in an examination are given in the table What would be the mean, median, and mode ...
GATE PI 2014
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A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard devi...
GATE PI 2014
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An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $...
GATE PI 2012
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A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, ...
GATE PI 2012
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It is estimated that the average number of events during a year is three. What is the probability of occurrence of not m...
GATE PI 2011
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Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin ha...
GATE PI 2010
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If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that ...
GATE PI 2010
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In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game ...
GATE PI 2008
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Two cards are drawn at random in succession with replacement from a deck of $$52$$ well shuffled cards Probability of ge...
GATE PI 2007
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If $$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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