1
GATE EE 2015 Set 1
Numerical
+2
-0
A random variable $$X$$ has probability density function $$f(x)$$ as given below:
$$$\,\,f\left( x \right) = \left\{ {\matrix{
{a + bx} & {for\,\,0 < x < 1} \cr
0 & {otherwise} \cr
} } \right.\,\,$$$
If the expected value $$\,\,E\left[ X \right] = 2/3,\,\,$$ then $$\,\,\Pr \left[ {X < 0.5} \right]\,\,$$ is __________.
If the expected value $$\,\,E\left[ X \right] = 2/3,\,\,$$ then $$\,\,\Pr \left[ {X < 0.5} \right]\,\,$$ is __________.
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2
GATE EE 2014 Set 2
Numerical
+2
-0
Consider a die with the property that the probability of a face with $$'n'$$ dots showing up is proportional to $$'n'.$$ The probability of the face with three dots showing up is _________.
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3
GATE EE 2014 Set 2
Numerical
+2
-0
Let $$X$$ be a random variable with probability density function $$f\left( x \right) = \left\{ {\matrix{
{0.2} & {for\,\left| x \right| \le 1} \cr
{0.1} & {for\,1 < \left| x \right| \le 4} \cr
0 & {otherwise} \cr
} } \right.$$
The probability $$P\left( {0.5 < x < 5} \right)$$ is _________.
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4
GATE EE 2014 Set 3
Numerical
+2
-0
Lifetime of an electric bulb is a random variable with density $$f\left( x \right) = k{x^2},$$ where $$x$$ is measured in years. If the minimum and maximum lifetimes of bulb are $$1$$ and $$2$$ years respectively, then the value of $$k$$ is ________.
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Questions Asked from Probability and Statistics (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits