1
GATE ECE 2020
Numerical
+2
-0
$X$ is a random variable with uniform probability density function in the interval $[-2,10]$. For $Y=2 X-6$, the conditional probability $P(Y \leq 7 \mid X \geq 5)$ (rounded off to three decimal places) is $\_\_\_\_$ .
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2
GATE ECE 2017 Set 2
Numerical
+2
-0
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $$40$$% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is ___________.
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3
GATE ECE 2016 Set 1
Numerical
+2
-0
Two random variables $$X$$ and $$Y$$ are distributed according to
$$${f_{X,Y}}\left( {x,y} \right) = \left\{ {\matrix{
{\left( {x + y} \right),} & {0 \le x \le 1,} & {0 \le y \le 1} \cr
{0,} & {otherwise} & \, \cr
} } \right.$$$
The probability $$P\left( {X + Y \le 1} \right)$$ is ________.
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4
GATE ECE 2016 Set 3
Numerical
+2
-0
The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a ''head'' is obtained. If the tosses are independent, then the probability of getting ''head'' for the first time in the fifth toss is ________.
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