1
GATE CE 2016 Set 2
+2
-0.6
If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$f\left( x \right) = \left\{ {\matrix{ {{x \over a} + 1} & : & { - a \le x < 0} \cr { - {x \over a} + 1} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$$$g\left( x \right) = \left\{ {\matrix{ { - {x \over a}} & : & { - a \le x < 0} \cr {{x \over a}} & : & {0 \le x \le a} \cr 0 & : & {otherwise} \cr } } \right.$$$

Which of the following statements is true?

A
Mean of $$f(x)$$ and $$g(x)$$ are same; Variance of $$f(x)$$ and $$g(x)$$ are same .
B
Mean of $$f(x)$$ and $$g(x)$$ are same ; Variance of $$f(x)$$ and $$g(x)$$ are different.
C
Mean of $$f(x)$$ and $$g(x)$$ are different ; Variance of $$f(x)$$ and $$g(x)$$ are same .
D
Mean of $$f(x)$$ and $$g(x)$$ are different; Variance of $$f(x)$$ and $$g(x)$$ are different.
2
GATE CE 2015 Set 2
Numerical
+2
-0
The probability density function of a random variable, $$x$$ is $$\matrix{ {f\left( x \right) = {x \over 4}\left( {4 - {x^2}} \right)} & {for\,\,0 \le x \le 2 = 0} \cr { = 0} & {otherwise} \cr }$$$The mean, $${\mu _x}$$ of the random variable is __________. Your input ____ 3 GATE CE 2015 Set 2 MCQ (Single Correct Answer) +2 -0.6 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? A $$4/52$$ B $$2/50$$ C $$\left( {1/52} \right) \times \left( {1/52} \right)$$ D $$\left( {1/52} \right) \times \left( {1/51} \right) \times \left( {1/50} \right)$$ 4 GATE CE 2015 Set 1 Numerical +2 -0 Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$p\left( {x,q} \right) = \left\{ {\matrix{ q & {if\,X = 0} \cr {1 - q} & {if\,X = 1} \cr 0 & {otherwise} \cr } } \right.$$$
$$q=0.4,$$ the variance of $$X$$ is _______.
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination