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Recent questions tagged probability-and-statistics
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GATE Electrical 2021 | Question: 27
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 $p/\left ( 1-p \right )$ $\left ( 1-p \right )/p$ $1/p$ $1/p^{2}$
Arjun
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Feb 20, 2021
by
Arjun
9.3k
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gateee-2021
probability-and-statistics
probability
0
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2
GATE Electrical 2019 | Question: 5
The mean-square of a zero-mean random process is $\frac{kT}{c},$ where $k$ is Boltzmann’s constant, $T$ is the absolute temperature, and $C$ is a capacitance. The standard deviation of the random process is $\frac{kT}{c} \\ $ $\sqrt{\frac{kT}{c}} \\ $ $\frac{c}{kT} \\ $ $\frac{\sqrt{kT}}{c}$
Arjun
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new
Feb 12, 2019
by
Arjun
9.3k
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gate2019-ee
probability-and-statistics
probability
standard-deviation
0
votes
0
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3
GATE Electrical 2019 | Question: 40
The probability of a resistor being deflective is $0.02$. There are $50$ such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is _______________
Arjun
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in
new
Feb 12, 2019
by
Arjun
9.3k
points
gate2019-ee
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
4
GATE Electrical 2012 | Question: 37
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
Andrijana3306
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Probability & Statistics
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
probability-and-statistics
probability
0
votes
0
answers
5
GATE Electrical 2012 | Question: 1
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that $\text{max}[X,Y]$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$
Andrijana3306
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Probability & Statistics
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
probability-and-statistics
probability
random-variable
uniform-distribution
0
votes
0
answers
6
GATE Electrical 2017 Set 2 | Question: 40
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 $Y$ denote the number of heads. The value of $\text{var} \{Y\}$, where $\text{var} \{ \cdot \}$ denotes the variance, equals $\frac{7}{8} \\$ $\frac{49}{64} \\$ $\frac{7}{64} \\$ $\frac{105}{64}$
Arjun
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new
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
probability-and-statistics
probability
random-variable
variance
1
vote
1
answer
7
GATE Electrical 2017 Set 2 | Question: 1
An urn contains $5$ red balls and $5$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a Red ball in the second draw is $\frac{1}{2} \\$ $\frac{4}{9} \\$ $\frac{5}{9} \\$ $\frac{6}{9} $
Arjun
asked
in
new
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
probability-and-statistics
probability
conditional-probability
0
votes
0
answers
8
GATE Electrical 2013 | Question: 11
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0< x< \infty$. then $P\{X> 1\}$ $0.368$ $0.5$ $0.632$ $1.0$
piyag476
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Probability & Statistics
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
probability-and-statistics
probability
random-variable
probability-density-function
0
votes
0
answers
9
GATE Electrical 2014 Set 3 | Question: 4
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of $k$ is ________.
makhdoom ghaya
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in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
probability-and-statistics
probability
random-variable
probability-density-function
numerical-answers
0
votes
0
answers
10
GATE Electrical 2014 Set 2 | Question: 27
Let $X$ be a random variable with probability density function $f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \text{otherwise } \end{cases} \\$ The probability $P(0.5 < X < 5)$ is ______.
makhdoom ghaya
asked
in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
probability-and-statistics
probability
random-variable
probability-density-function
numerical-answers
2
votes
1
answer
11
GATE Electrical 2014 Set 2 | Question: 2
Consider a dice with the property that the probability of a face with $n$ dots showing up is proportional to $n$. The probability of the face with three dots showing up is ________.
makhdoom ghaya
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in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
probability-and-statistics
probability
1
vote
0
answers
12
GATE Electrical 2014 Set 1 | Question: 27
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is $2^{-n}$ $0$ $^{n}C_{n-3}2^{-n}$ $2^{-n+3}$
makhdoom ghaya
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in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
probability-and-statistics
probability
coins
0
votes
0
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13
GATE Electrical 2015 Set 2 | Question: 27
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the ... is TRUE? The coin tosses are independent. $R$ is fair, $S$ is not. $S$ is fair, $R$ is not. The coin tosses are dependent.
makhdoom ghaya
asked
in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
probability-and-statistics
probability
0
votes
1
answer
14
GATE Electrical 2015 Set 1 | Question: 29
Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is $5/11$ $1/2$ $7/13$ $6/11$
makhdoom ghaya
asked
in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-1
probability-and-statistics
probability
conditional-probability
0
votes
0
answers
15
GATE Electrical 2015 Set 1 | Question: 1
A random variable $X$ has probability density function $f(x)$ as given below: $ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$ If the expected value $E[x] = 2/3$, then $Pr[x < 0.5]$ is __________.
makhdoom ghaya
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in
Probability & Statistics
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-1
probability-and-statistics
probability
random-variable
probability-density-function
expectation
numerical-answers
0
votes
0
answers
16
GATE Electrical 2016 Set 2 | Question: 33
Let the probability density function of a random variable, $X$, be given as: $f_{x}(x)=\frac{3}{2}e^{-3x}u(x)+ae^{4x}u(-x)$ where u(x) is the unit step function. Then the value of 'a' and prob $\left\{X \leq 0\right\}$, respectively are $2, \frac{1}{2}$ $4, \frac{1}{2}$ $2, \frac{1}{4}$ $4, \frac{1}{4}$
makhdoom ghaya
asked
in
Probability & Statistics
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
probability-and-statistics
probability
random-variable
probability-density-function
0
votes
0
answers
17
GATE Electrical 2016 Set 1 | Question: 26
Candidates were asked to come to an interview with $3$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $3$ pens having the same colour is _________.
makhdoom ghaya
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in
Probability & Statistics
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
probability-and-statistics
probability
conditional-probability
numerical-answers
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