1
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 _______.
Your input ____
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 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
A
$$1$$
B
$$0.5$$
C
$$\pi $$
D
$${\pi \over 2}$$
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