1
GATE ECE 2014 Set 1
Numerical
+2
-0
The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $$\left\{ {0 \le y \le x} \right.$$ and $$\,\left. {0 \le x \le 12} \right\}$$ is _________.
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2
GATE ECE 2014 Set 1
Numerical
+2
-0
Let $$\,{X_1},\,\,{X_2}\,\,$$ and $$\,{X_3}\,$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,1} \right].$$ The probability $$p$$ {$${X_1}$$ is the largest} is __________.
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3
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mean values of $$X$$ and $${{X^2}}$$, respectively. The relation which always holds true is
A
$${\left( {E\left[ X \right]} \right)^2} > E\left[ {X{}^2} \right]$$
B
$$E\left[ {X{}^2} \right] \ge {\left( {E\left[ X \right]} \right)^2}$$
C
$$E\left[ {X{}^2} \right] = {\left( {E\left[ X \right]} \right)^2}$$
D
$$E\left[ {X{}^2} \right] > {\left( {E\left[ X \right]} \right)^2}$$
4
GATE ECE 2014 Set 1
Numerical
+1
-0
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _______.
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