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Previous Years Questions
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Marks 1
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The probability that a thermistor randomly picked up from a production unit is defective is $$0.1.$$ The probability th...
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A continuous random variable $$X$$ has a probability density function $$f\left( x \right) = {e^{ - x}},0 < x < \in...
GATE IN 2013
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Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ ...
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A screening test is carried out to detect a certain disease. It is found that $$12$$% of the positive reports and $$15$...
GATE IN 2009
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A random variable is uniformly distributed over the interval $$2$$ to $$10.$$ Its variance will be
GATE IN 2008
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Assume that the duration in minutes of a telephone conversation follows the exponential distribution $$\,f\left( x \righ...
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The probability that there are $$53$$ Sundays in a randomly chosen leap year is
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Marks 2
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The probability that a communication system will have high fidelity is $$0.81.$$ The probability that the system will h...
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An urn contains $$5$$ red and $$7$$ green balls. A ball is drawn at random and its colour is noted. The ball is placed b...
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A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event...
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The probability density function of a random variable $$X$$ is $$\,{P_x}\left( x \right) = {e^{ - x}}\,\,$$ for $$\,\,x...
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The figure shown the schematic of a production process with machines $$A, B$$ and $$C.$$ An input job needs to be pre-pr...
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Given that $$x$$ is a random variable in the range $$\left[ {0,\infty } \right]$$ with a probability density function $$...
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A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd...
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The box $$1$$ contains chips numbered $$3, 6, 9,$$ $$12$$ and $$15$$. The box $$2$$ contains chips numbered $$6, 11, 16...
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$${P_x}\left( X \right) = M{e^{\left( { - 2\left| x \right|} \right)}} + N{e^{\left( { - 3\left| x \right|} \right)}}\,\...
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Consider a Gaussian distributed random variable with zero mean and standard deviation $$\sigma .\,\,\,$$ The value of it...
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