GATE IN
Engineering Mathematics
Probability and Statistics
Previous Years Questions

## Marks 1

The probability that a thermistor randomly picked up from a production unit is defective is $$0.1.$$ The probability that out of $$10$$ thermistors r...
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 screening test is carried out to detect a certain disease. It is found that $$12$$% of the positive reports and $$15$$% of the negative reports ar...
A random variable is uniformly distributed over the interval $$2$$ to $$10.$$ Its variance will be
Assume that the duration in minutes of a telephone conversation follows the exponential distribution $$\,f\left( x \right) = {1 \over 5}{e^{ - x/5}},\... The probability that there are$$53$$Sundays in a randomly chosen leap year is ## Marks 2 The probability that a communication system will have high fidelity is$$0.81.$$The probability that the system will have both high fidelity and hig... An urn contains$$5$$red and$$7$$green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with an... The probability density function of a random variable$$X$$is$$\,{P_x}\left( x \right) = {e^{ - x}}\,\,$$for$$\,\,x \ge 0\,\,$$and$$0$$otherw... A coin is tossed thrice. Let$$X$$be the event that head occurs in each of the first two tosses. Let$$Y$$be the event that a tail occurs on the thi... Given that$$x$$is a random variable in the range$$\left[ {0,\infty } \right]$$with a probability density function$${{{e^{ - {x \over 2}}}} \over ...
The figure shown the schematic of a production process with machines $$A, B$$ and $$C.$$ An input job needs to be pre-processed either by $$A$$ or by ...
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
The box $$1$$ contains chips numbered $$3, 6, 9,$$ $$12$$ and $$15$$. The box $$2$$ contains chips numbered $$6, 11, 16, 21$$ and $$26$$. Two chips,...
Consider a Gaussian distributed random variable with zero mean and standard deviation $$\sigma .\,\,\,$$ The value of its cumulative distribution func...
$${P_x}\left( X \right) = M{e^{\left( { - 2\left| x \right|} \right)}} + N{e^{\left( { - 3\left| x \right|} \right)}}\,\,$$ is the probability densit...
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