## 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...