1
GATE CE 2017 Set 1
+2
-0.6
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 is correct?
A
$$a = 1,\,b = 4$$
B
$$\,a = 0.5,\,b = 1$$
C
$$a=0,$$ $$b=1$$
D
$$a=1,$$ $$b=-1$$
2
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.
3
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 __________.
4
GATE CE 2015 Set 2
+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
$$\left( {1/52} \right) \times \left( {1/51} \right) \times \left( {1/50} \right)$$
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
NEET