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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 2021
MCQ (Single Correct Answer)
+2
-0.67

Suppose the probability that a coin toss shows "head" is $p$, where $0 < p < 1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is :

A

$\frac{p}{1-p}$

B

$\frac{1-p}{p}$

C

$\frac{1}{p}$

D

$\frac{1}{p^2}$

4
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
$${105 \over 64}$$
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