1
GATE ECE 2014 Set 1
Numerical
+2
-0
Let $$\,{X_1},\,\,{X_2}\,\,$$ and $$\,{X_3}\,$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,1} \right].$$ The probability $$p$$ {$${X_1}$$ is the largest} is __________.
2
GATE ECE 2013
+2
-0.6
Let $$U$$ and $$V$$ be two independent zero mean Gaussian random variables of variances $${1 \over 4}$$ and $${1 \over 9}$$ respectively. The probability $$\,P\left( {3V \ge 2U} \right)\,\,$$ is
A
$$4/9$$
B
$$1/2$$
C
$$2/3$$
D
$$5/9$$
3
GATE ECE 2013
+2
-0.6
Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution functions of $$U$$ and $$2V$$ be $$F(x)$$ and $$G(x)$$ respectively. Then for all values of $$x$$
A
$$F\left( x \right) - G\left( x \right) \le 0$$
B
$$F\left( x \right) - G\left( x \right) \ge 0$$
C
$$\left( {F\left( x \right) - G\left( x \right)} \right).x \le 0$$
D
$$\left( {F\left( x \right) - G\left( x \right)} \right).x \ge 0$$
4
GATE ECE 2012
+2
-0.6
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
A
$$1/3$$
B
$$1/2$$
C
$$2/3$$
D
$$3/4$$
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