GATE PI
Engineering Mathematics
Probability and Statistics
Previous Years Questions

## Marks 1

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

## Marks 2

A normal random variable $$X$$ has the following probability density function $${f_x}\left( x \right) = {1 \over {\sqrt {8\pi } }}e{}^{ - \left\{ {{... A product is an assemble of$$5$$different components. The product can be sequentially assembled in two possible ways. If the$$5$$components are pl... A coin is tossed thrice. Let$$X$$be the event that head occurs in each of the first two tosses. Let$$Y$$be the event that a tail occurs on the thi... A simple random sample of$$100$$observations was taken form a large population. The sample mean and the standard deviation were determined to be$$...
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...
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...
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the s...
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...
If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that $$X > 2$$ is
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...
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...
If $$X$$ is a continuous random variable whose probability density function is given by $$\,\,\,f\left( x \right) = \left\{ {\matrix{ {k\left( {5... Two cards are drawn at random in succession with replacement from a deck of$$52 well shuffled cards Probability of getting both 'Aces' is
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