1
GATE IN 2017
+2
-0.6
The probability that a communication system will have high fidelity is $$0.81.$$ The probability that the system will have both high fidelity and high selectivity is $$0.18$$. The probability that a given system with high fidelity will have high selectivity is
A
$$0.181$$
B
$$0.191$$
C
$$0.222$$
D
$$0.826$$
2
GATE IN 2016
+2
-0.6
An urn contains $$5$$ red and $$7$$ green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is
A
$${{65} \over {156}}$$
B
$${{67} \over {156}}$$
C
$${{79} \over {156}}$$
D
$${{89} \over {156}}$$
3
GATE IN 2015
Numerical
+2
-0
The probability density function of a random variable $$X$$ is $$\,{P_x}\left( x \right) = {e^{ - x}}\,\,$$ for $$\,\,x \ge 0\,\,$$ and $$0$$ otherwise. The expected value of the function $$\,{g_x}\left( x \right) = {e^{3x/4}}$$ is___________.
4
GATE IN 2015
+2
-0.6
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
A
$$X$$ and $$Y$$ are not independent
B
$$Y$$ and $$Z$$ are dependent
C
$$Y$$ and $$Z$$ are independent
D
$$X$$ and $$Z$$ are independent
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