1
GATE EE 2022
Numerical
+1
-0.33

Let the probability density function of a random variable x be given as

f(x) = ae$$-$$2|x|

The value of a is _________.

2
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
An urn contains $$5$$ red balls and $$5$$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
A
$${1 \over 2}$$
B
$${4 \over 9}$$
C
$${5 \over 9}$$
D
$${6 \over 9}$$
3
GATE EE 2017 Set 2
Numerical
+1
-0
Assume that in a traffic junction, the cycle of the traffic signal lights is $$2$$ minutes of green (vehicle does not stop) and $$3$$ minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over $$5$$ minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is _________.
4
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Two coins $$R$$ and $$S$$ are tossed. The $$4$$ joint events $$\,\,\,\,\,\,{H_R}{H_S},\,\,\,\,{T_R}{T_S},\,\,\,\,{H_R}{T_S},\,\,\,\,{T_R}{H_S}\,\,\,\,\,\,\,$$ have probabilities $$0.28,$$ $$0.18,$$ $$0.30,$$ $$0.24$$ respectively, where $$H$$ represents head and $$T$$ represents tail. Which one of the following is TRUE?
A
The coin tosses are independent
B
$$R$$ is fair, $$S$$ is not
C
$$S$$ is fair, $$R$$ is not
D
The coin tosses are dependent
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