GATE EE
Engineering Mathematics
Probability and Statistics
Previous Years Questions

## Marks 1

Let the probability density function of a random variable x be given as f(x) = ae$$-$$2|x| The value of a is _________....
An urn contains $$5$$ red balls and $$5$$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The ...
Assume that in a traffic junction, the cycle of the traffic signal lights is $$2$$ minutes of green (vehicle does not stop) and $$3$$ minutes of red (...
Two coins $$R$$ and $$S$$ are tossed. The $$4$$ joint events $$\,\,\,\,\,\,{H_R}{H_S},\,\,\,\,{T_R}{T_S},\,\,\,\,{H_R}{T_S},\,\,\,\,{T_R}{H_S}\,\,\,\,... A fair coin is tossed$$n$$times. The probability that the difference between the number of heads and tails is$$(n-3)$$is A continuous random variable$$X$$has a probability density function$$f\left( x \right) = {e^{ - x}},0 < x < \infty .$$Then$$P\left\{ {X &g...
Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\le... A box contains$$4$$white balls and$$3$$red balls. In succession, two balls are randomly selected and removed from the box. Given that first remove... Assume for simplicity that$$N$$people, all born in April (a month of$$30$$days) are collected in a room, consider the event of at least two people...$$X$$is uniformly distributed random variable that take values between$$0$$and$$1.$$The value of$$E\left( {{X^3}} \right)$$will be If$$P$$and$$Q$$are two random events, then which of the following is true? ## Marks 2 A person decides to toss a fair coin repeatedly until he gets a head. He will make at most$$3$$tosses. Let the random variable$$Y$$denotes the num... Let the probability density function of a random variable$$X,$$be given as:$$\${f_x}\left( x \right) = {3 \over 2}{e^{ - 3x}}u\left( x \right) + a{...
Candidates were asked to come to an interview with $$3$$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could...
Two players, $$A$$ and $$B,$$ alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $$A$$ starts the ga...
A random variable $$X$$ has probability density function $$f(x)$$ as given below: $$\,\,f\left( x \right) = \left\{ {\matrix{ {a + bx} & {for... Given Set$$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$and Set$$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$two numbers are randomly selec... The probabilities that a student passes in Mathematics, Physics and Chemistry are$$m, p$$and$$c$$respectively. Of these subjects, the student has ... Lifetime of an electric bulb is a random variable with density$$f\left( x \right) = k{x^2},$$where$$x$$is measured in years. If the minimum and m... Consider a die with the property that the probability of a face with$$'n'$$dots showing up is proportional to$$'n'.$$The probability of the face w... Let$$X$$be a random variable with probability density function$$f\left( x \right) = \left\{ {\matrix{ {0.2} & {for\,\left| x \right| \le 1} ...
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses...
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