# Probability and Statistics · Engineering Mathematics · GATE PI

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## Marks 1

GATE PI 2016
A fair coin is tossed $$N$$ times. The probability that head does not turn up in any of the tosses is
GATE PI 2014
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 loss on that day is $$80$$%. ...
GATE PI 2008
For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean is $$\,\mu = 100\,\,.$$ If ...
GATE PI 2007
The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 + 3P} \over 5}\,\,$$ and $$\,\,... GATE PI 2005 Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds$$8$$is GATE PI 2005 The life of a bulb (in hours) is a random variable with an exponential distribution$$\,\,f\left( t \right) = \alpha {e^{ - \alpha t}},0 \le t \le \in...

## Marks 2

GATE PI 2016
A normal random variable $$X$$ has the following probability density function $${f_x}\left( x \right) = {1 \over {\sqrt {8\pi } }}e{}^{ - \left\{ {{... GATE PI 2015 A product is an assemble of$$5$$different components. The product can be sequentially assembled in two possible ways. If the$$5$$components are pl... GATE PI 2015 A coin is tossed thrice. Let$$X$$be the event that head occurs in each of the first two tosses. Let$$Y$$be the event that a tail occurs on the thi... GATE PI 2014 A simple random sample of$$100$$observations was taken form a large population. The sample mean and the standard deviation were determined to be$$...
GATE PI 2014
Marks obtained by $$100$$ students in an examination are given in the table What would be the mean, median, and mode of the marks obtained by the s...
GATE PI 2012
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The proba...
GATE PI 2012
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the s...
GATE PI 2011
It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two...
GATE PI 2010
If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that $$X > 2$$ is
GATE PI 2010
Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and on...
GATE PI 2008
In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Assuming that p...
GATE PI 2007
If $$X$$ is a continuous random variable whose probability density function is given by $$\,\,\,f\left( x \right) = \left\{ {\matrix{ {k\left( {5... GATE PI 2007 Two cards are drawn at random in succession with replacement from a deck of$$52 well shuffled cards Probability of getting both 'Aces' is
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