1
GATE EE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let the probability density function of a random variable $$X,$$ be given as: $${f_x}\left( x \right) = {3 \over 2}{e^{ - 3x}}u\left( x \right) + a{e^{4x}}u\left( { - x} \right)$$$where $$u(x)$$ is the unit step function. Then the value of $$'a'$$ and Prob $$\left\{ {X \le 0} \right\},$$ respectively, are A $$2,{1 \over 2}$$ B $$4,{1 \over 2}$$ C $$2,{1 \over 4}$$ D $$4,{1 \over 4}$$ 2 GATE EE 2016 Set 1 Numerical +2 -0 Candidates were asked to come to an interview with $$3$$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $$3$$ pens having the same colour is _______. Your input ____ 3 GATE EE 2015 Set 1 MCQ (Single Correct Answer) +2 -0.6 Two players, $$A$$ and $$B,$$ alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $$A$$ starts the game, the probability that $$A$$ wins the game is A $$5/11$$ B $$1/2$$ C $$7/13$$ D $$6/11$$ 4 GATE EE 2015 Set 1 Numerical +2 -0 A random variable $$X$$ has probability density function $$f(x)$$ as given below: $$\,\,f\left( x \right) = \left\{ {\matrix{ {a + bx} & {for\,\,0 < x < 1} \cr 0 & {otherwise} \cr } } \right.\,\,$$$
If the expected value $$\,\,E\left[ X \right] = 2/3,\,\,$$ then $$\,\,\Pr \left[ {X < 0.5} \right]\,\,$$ is __________.
Your input ____
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