Probability and Statistics · Engineering Mathematics · GATE CE

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. ...

Which of the following probability distribution functions (PDFs) has the mean greater than the median? ...

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without polluti...

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A ...

A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following...

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

The spot speeds (expressed in km/hr) observed at a road section are $$66, 62, 45, 79, 32, 51, 56, 60, 53$$ and $$49.$$ The median speed (expressed in ...

$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right) = 0.7.$$ Which one of the fol...

Type $${\rm I}{\rm I}$$ error in hypothesis testing is

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes; (i) Head, (ii) Head, (III) Head, (iv) Head. The pro...

The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200$$ mm, respectively. The proba...

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing

Three values of $$x$$ and $$y$$ are to be fitted in a straight line in the form $$y=a+bx$$ by the method of least squares. Given $$\,\,\,\sum x = 6,\...

If the standard deviation of the speed of vehicles in a highway is $$8.8$$ kmph and the mean speed of the vehicles is $$33$$ kmph, the coefficient of...

A box contains $$10$$ screws, $$3$$ of which are defective. Two screws are drawn at random with replacement. The probability that none of the two scre...

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X red...

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the proba...

A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _...

For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements...

If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$$f\left( x \right) = \left\{ {\matrix{ {{x \over a} + 1} & : & { - a \le...

Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$$p\left( {x,q} \right) = \left\{ {\matrix{ q & {if\,X =...

Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability that the third card is a king?

The probability density function of a random variable, $$x$$ is $$$\matrix{ {f\left( x \right) = {x \over 4}\left( {4 - {x^2}} \right)} & {for...

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E \right) = \left\{ {\matrix{ ...

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is...

An observer counts $$240$$veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probabilit...

If $$\left\{ x \right\}$$ is a continuous, real valued random variable defined over the interval $$\left( { - \infty ,\,\, \pm \infty } \right)$$ and ...

Find the value of $$\lambda $$ such that the function $$f(x)$$ is a valid probability density function ________.

Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball...

The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}...

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed...