1
GATE EE 2023
Numerical
+2
-0

The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).

Your input ____
2
GATE EE 2022
Numerical
+2
-0

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

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

The value of a is _________.

Your input ____
3
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $$3$$ tosses. Let the random variable $$Y$$ denotes the number of heads. The value of var $$\left\{ Y \right\},$$ where var $$\left\{ . \right\}$$ denotes the variance, equal
A
$${7 \over 8}$$
B
$${49 \over 64}$$
C
$${7 \over 64}$$
D
$${105 \over 64}$$
4
GATE EE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let the probability density function of a random variable $$X,$$ be given as: $$${f_x}\left( x \right) = {3 \over 2}{e^{ - 3x}}u\left( x \right) + a{e^{4x}}u\left( { - x} \right)$$$
where $$u(x)$$ is the unit step function. Then the value of $$'a'$$ and Prob $$\left\{ {X \le 0} \right\},$$ respectively, are
A
$$2,{1 \over 2}$$
B
$$4,{1 \over 2}$$
C
$$2,{1 \over 4}$$
D
$$4,{1 \over 4}$$
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