1

GATE CE 2014 Set 1

Numerical

+2

-0

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by
$$$f\left( E \right) = \left\{ {\matrix{
{{1 \over 5}} & {0 \le E \le 5\,mm/day} \cr
0 & {otherwise} \cr
} } \right.$$$

The probability that $$E$$ lies in between $$2$$ and $$4$$ $$mm/day$$ in the watershed is (in decimal) _______.

The probability that $$E$$ lies in between $$2$$ and $$4$$ $$mm/day$$ in the watershed is (in decimal) _______.

Your input ____

2

GATE CE 2014 Set 1

Numerical

+2

-0

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 independent and follows a Poisson distribution. The probability that there will be less than $$4$$ penalties in a day is ________.

Your input ____

3

GATE CE 2014 Set 2

Numerical

+2

-0

An observer counts $$240$$veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a $$30$$-second time interval is _______.

Your input ____

4

GATE CE 2014 Set 2

MCQ (Single Correct Answer)

+2

-0.6

If $$\left\{ x \right\}$$ is a continuous, real valued random variable defined over the interval $$\left( { - \infty ,\,\, \pm \infty } \right)$$ and its occurrence is defined by the density function given as: $$f\left( x \right) = {1 \over {\sqrt {2\pi * b} }}{e^{ - {1 \over 2}{{\left( {{{x - a} \over b}} \right)}^2}}}$$ where $$'a'$$ and $$'b'$$ are the statistical attributes of the random variable $$\left\{ x \right\}$$. The value of the integral $$\int\limits_{ - \infty }^a {{1 \over {\sqrt {2\pi * b} }}{e^{ - {1 \over 2}{{\left( {{{x - a} \over b}} \right)}^2}}}} dx\,\,\,$$ is

Questions Asked from Probability and Statistics (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude