1
GATE CE 2014 Set 2
+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
A
$$1$$
B
$$0.5$$
C
$$\pi$$
D
$${\pi \over 2}$$
2
GATE CE 2013
Numerical
+2
-0
Find the value of $$\lambda$$ such that the function $$f(x)$$ is a valid probability density function ________.
3
GATE CE 2012
+2
-0.6
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
A
$${1 \over {32}}$$
B
$${2 \over {32}}$$
C
$${3 \over {32}}$$
D
$${6 \over {32}}$$
4
GATE CE 2011
+2
-0.6
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 is drawn at random from each container. The probability that one of the balls is red and the other is blue will be ___________.
A
$${1 \over 7}$$
B
$${9 \over 49}$$
C
$${12 \over 49}$$
D
$${3 \over 7}$$
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
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
EXAM MAP
Joint Entrance Examination