1
GATE ECE 2014 Set 3
+1
-0.3
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
A
$$0.067$$
B
$$0.073$$
C
$$0.082$$
D
$$0.091$$
2
GATE ECE 2014 Set 1
+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
$$E\left[ {X{}^2} \right] > {\left( {E\left[ X \right]} \right)^2}$$
3
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 _______.
4
GATE ECE 2012
+1
-0.3
Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less than $$1/2$$ is
A
$$3/4$$
B
$$9/16$$
C
$$1/4$$
D
$$2/3$$
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