1
GATE IN 2011
+2
-0.6
The box $$1$$ contains chips numbered $$3, 6, 9,$$ $$12$$ and $$15$$. The box $$2$$ contains chips numbered $$6, 11, 16, 21$$ and $$26$$. Two chips, one from each box are drawn at random. The numbers written on these chips are multiplied. The probability for the product to be an even number is ______________.
A
$${6 \over {25}}$$
B
$${2 \over {5}}$$
C
$${3 \over {5}}$$
D
$${19 \over {25}}$$
2
GATE IN 2008
+2
-0.6
Consider a Gaussian distributed random variable with zero mean and standard deviation $$\sigma .\,\,\,$$ The value of its cumulative distribution function at the origin will be
A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$10\,\sigma$$
3
GATE IN 2008
+2
-0.6
$${P_x}\left( X \right) = M{e^{\left( { - 2\left| x \right|} \right)}} + N{e^{\left( { - 3\left| x \right|} \right)}}\,\,$$ is the probability density function for the real random variable $$X,$$ over the entire $$x$$-axis, $$M$$ and $$N$$ are both positive real numbers. The equation relating $$M$$ and $$N$$ is
A
$$M + {2 \over 3}N = 1$$
B
$$2M + {1 \over 3}N = 1$$
C
$$M+N=1$$
D
$$M+N=3$$
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