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Recent questions tagged probability
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GATE2020EC: 12
A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of its bits is decoded wrongly. The ... $\alpha ^{N}$ $1\alpha ^{N}$ $1\left ( 1\alpha \right )^{N}$
asked
Feb 13
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by
jothee
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gate2020ec
probability
digitalcommunications
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2
GATE2020EC: 22
A binary random variable $X$ takes the value $+2$ or $2$. The probability $P(X=+2)=\alpha $. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is maximum, is __________.
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Feb 13
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jothee
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gate2020ec
numericalanswers
probability
engineeringmathematics
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3
GATE2016 EC3: 3
The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _________
asked
Nov 21, 2019
in
Probability and Statistics
by
KUSHAGRA गुप्ता
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260
points)
gate2016ec
probability
0
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4
GATE2009 EC: 11
A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads. (A) $\left(\dfrac{1}{2}\right)^{2}$ (B) $^{10}C_2\left(\dfrac{1}{2}\right)^{2}$ (C) $\left(\dfrac{1}{2}\right)^{10}$ (D) $^{10}C_2\left(\dfrac{1}{2}\right)^{10}$
asked
Nov 21, 2019
in
Probability and Statistics
by
KUSHAGRA गुप्ता
(
260
points)
gate2009ec
probability
0
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0
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5
GATE2019 EC: 47
A random variable $X$ takes values $1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is independent of ... the probability of error $Pr[ \hat{X} \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is _________.
asked
Feb 12, 2019
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by
Arjun
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1.4k
points)
gate2019ec
numericalanswers
probability
engineeringmathematics
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0
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6
GATE201633
The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _______
asked
Mar 28, 2018
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by
Milicevic3306
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15.7k
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gate2016ec3
numericalanswers
probability
engineeringmathematics
0
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0
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7
GATE2016322
An analog baseband signal, bandlimited to $100\ Hz$, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is _______
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Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2016ec3
numericalanswers
controlsystems
nyquist
probability
0
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0
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8
GATE2016351
The bit error probability of a memoryless binary symmetric channel is $10^{5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be in error is _______
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec3
numericalanswers
probability
engineeringmathematics
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0
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9
GATE2016221
A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},\frac{1}{8}\right \}.$ The minimum required average codeword length in bits to represent this source for errorfree reconstruction is _________
asked
Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2016ec2
numericalanswers
probability
engineeringmathematics
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0
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10
GATE2016228
Two random variables $X$ and $Y$ are distributed according to $f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$ The probability $P(X+Y\leq 1)$ is ________
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Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2016ec2
numericalanswers
probability
engineeringmathematics
0
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0
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11
GATE2016248
An information source generates a binary sequence $\left \{ \alpha _{n} \right \}$. $\alpha _{n}$ can take one of the two possible values $1$ and $+1$ with equal probability and are statistically independent and identically distributed. This sequence is precoded to obtain another ... If there is a null at $f=\frac{1}{3T}$ in the power spectral density of $X(t)$, then $k$ is ________
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Mar 28, 2018
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by
Milicevic3306
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15.7k
points)
gate2016ec2
numericalanswers
probability
engineeringmathematics
0
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0
answers
12
GATE2016148
Consider a discrete memoryless source with alphabet $S = \{s_0,s_1,s_2,s_3,s_4, \dots \}$ and respective probabilities of occurence $P = \bigg\{ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots \bigg\}$. The entropy of the source (in bits) is _________
asked
Mar 28, 2018
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by
Milicevic3306
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15.7k
points)
gate2016ec1
numericalanswers
probability
engineeringmathematics
0
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0
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13
GATE201513
Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements is FALSE? $P(A \cap B) = P(A)P(B)$ $P(A \mid B) = P(A)$ $P(A \cup B) = P(A) + P(B)$ $P(\overline{A} \cap \overline{B} )= P(\overline{A})P(\overline{B})$
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Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2015ec1
probability
engineeringmathematics
0
votes
0
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14
GATE2015149
The input $X$ to the Binary Symmetric Channel (BSC) shown in the figure is $’1’$ with probability $0.8$. The crossover probability is $1/7$. If the received bit $Y=0$, the conditional probability that $’1’$ was transmitted is ____________
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Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2015ec1
numericalanswers
probability
engineeringmathematics
0
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0
answers
15
GATE2015152
A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides for either $0$ or $1$ based on the received value $R$. It is given that the conditional density ... $0$ $1/12$ $1/9$ $1/6$
asked
Mar 28, 2018
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by
Milicevic3306
(
15.7k
points)
gate2015ec1
probability
engineeringmathematics
0
votes
0
answers
16
GATE2014427
Parcels from sender S to receiver R pass sequentially through twopost offices. Each postoffice has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is _________
asked
Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec4
numericalanswers
probability
engineeringmathematics
0
votes
0
answers
17
GATE2014450
Consider the $Z$channel given in the figure. The input is $0$ or $1$ with equal probability. If the output is $0$, the probability that the input is also $0$ equals ___________
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec4
numericalanswers
probability
engineeringmathematics
0
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0
answers
18
GATE201434
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is $0.067$ $0.073$ $0.082$ $0.091$
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec3
probability
engineeringmathematics
0
votes
0
answers
19
GATE2014329
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1]$. The probability $P\left \{ X_{1}+X_{2}\leq X_{3}\right \}$ is _________.
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec3
numericalanswers
probability
engineeringmathematics
0
votes
0
answers
20
GATE2014352
A binary random variable $X$ takes the value of $1$ with probability $1/3$. $X$ is input to a cascade of $2$ independent identical binary symmetric channels (BSCs) each with crossover probability $1/2$. The output of BSCs are the random variables $Y_{1}$ and $Y_{2}$ as shown in the figure. The value of $H( Y_{1} )+H( Y_{2} )$ in bits is ______.
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Mar 26, 2018
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Milicevic3306
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15.7k
points)
gate2014ec3
numericalanswers
probability
engineeringmathematics
0
votes
0
answers
21
GATE2014249
The input to a $1$ – bit quantizer is a random variable $X$ with pdf $f_{X}( x )= 2e^{2x}$ for $x\geq 0$ and $f_{X} (x )= 0$ for $x< 0$. For outputs to be of equal probability, the quantizer threshold should be ______.
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec2
numericalanswers
probability
0
votes
0
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22
GATE20141GA10
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $1/4$ $1/3$ $1/2$ $2/3$
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Mar 26, 2018
in
Numerical Ability
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Milicevic3306
(
15.7k
points)
gate2014ec1
numericalability
probability
0
votes
0
answers
23
GATE201415
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is the largest}\}$ is ________.
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec1
numericalanswers
probability
0
votes
0
answers
24
GATE2014123
The capacity of a Binary Symmetric Channel $\text{(BSC)}$ with crossover probability $0.5$ is ________.
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec1
numericalanswers
probability
0
votes
0
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25
GATE201365
What is the chance that a leap year, selected at random, will contain $53$ Saturdays? $2/7$ $3/7$ $1/7$ $5/7$
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Mar 26, 2018
in
Numerical Ability
by
Milicevic3306
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15.7k
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gate2013ec
numericalability
probability
leapyear
0
votes
0
answers
26
GATE201338
Consider two identically distributed zeromean 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 $x$ $F(x)  G(x) \leq 0$ $F(x)  G(x) \geq 0$ $(F(x)  G(x)) \cdot x\leq 0$ $(F(x)  G(x)) \cdot x\geq 0$
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Mar 26, 2018
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by
Milicevic3306
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15.7k
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gate2013ec
probability
0
votes
0
answers
27
GATE201326
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
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Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.7k
points)
gate2013ec
probability
randomvariable
0
votes
1
answer
28
GATE201236
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$
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Mar 25, 2018
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Milicevic3306
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15.7k
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gate2012ec
probability
engineeringmathematics
0
votes
0
answers
29
GATE201238
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probability of error for an optimum receiver will be $\frac{7}{80}$ $\frac{63}{80}$ $\frac{9}{10}$ $\frac{1}{10}$
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Mar 25, 2018
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Milicevic3306
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15.7k
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gate2012ec
probability
engineeringmathematics
0
votes
0
answers
30
GATE201224
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
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Mar 25, 2018
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Milicevic3306
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15.7k
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gate2012ec
probability
engineeringmathematics
0
votes
0
answers
31
GATE201215
A source alphabet consists of $N$ symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $\varepsilon$ and decreases that of the second by $\varepsilon$. After encoding, the entropy of the source increases remains the same increases only if $N=2$ decreases
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Mar 25, 2018
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Milicevic3306
(
15.7k
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gate2012ec
probability
engineeringmathematics
0
votes
1
answer
32
GATE2018GA9
A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. 85% of cabs in the city are green and the remaining cabs are blue. A witness identified the cab involved in the ... the tune. Which of the following options is closest to the probability that the accident was caused by a blue cab? 12% 15% 41% 80%
asked
Feb 19, 2018
in
Numerical Ability
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gatecse
(
1.4k
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gate2018ec
numericalability
probability
0
votes
0
answers
33
GATE201823
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
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Feb 19, 2018
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gatecse
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1.4k
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gate2018ec
numericalanswers
probability
engineeringmathematics
+1
vote
0
answers
34
GATE2017 EC2: 29
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________
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Nov 23, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)
gate2017ec2
numericalanswers
probability
engineeringmathematics
0
votes
0
answers
35
GATE2017 EC2: 22
Consider the random process $X(t)=U+Vt,$ Where $U$ is a zeromean Gaussian random variable and V is a random variable uniformly distributed between $0$ and $2$. Assume that $U$ and $V$ are statistically independent. The mean value of the random process at $t = 2$ is ________
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Nov 23, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)
gate2017ec2
numericalanswers
probability
engineeringmathematics
0
votes
0
answers
36
GATE2017 EC1: 4
Three fair cubical dice are thrown simultaneously . The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place)________.
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Nov 17, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)
gate2017ec1
probability
numericalanswers
engineeringmathematics
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