1
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 ________.

2
GATE ECE 2015 Set 2
+2
-0.6
Let $$\,\,X \in \left\{ {0,1} \right\}\,\,$$ and $$\,\,Y \in \left\{ {0,1} \right\}\,\,$$ be two independent binary random variables. If $$\,\,P\left( {X\,\, = 0} \right) = p\,\,$$ and $$\,\,P\left( {Y\,\, = 0} \right) = q\,\,$$, then $$P\left( {X + Y \ge 1} \right)$$ is equal to
A
$$pq+(1-p)(1-q)$$
B
$$pq$$
C
$$p(1-q)$$
D
$$1-pq$$
3
GATE ECE 2015 Set 3
Numerical
+2
-0
A fair die with faces $$\left\{ {1,2,3,4,5,6} \right\}$$ is thrown repeatedly till $$'3'$$ is observed for the first time. Let $$X$$ denote the number of times the dice is thrown. The expected value of $$X$$ is _________.
4
GATE ECE 2015 Set 1
Numerical
+2
-0
The input $$X$$ to the Binary Symmetric Channel (BSC) shown in the figure is $$'1'$$ with probability $$0.8.$$ The cross-over probability is $$1/7$$. If the received bit $$Y=0,$$ the conditional probability that $$'1'$$ was transmitted is _______.