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Recent questions and answers in Probability and Statistics
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GATE Mechanical 2021 Set 2 | Question: 3
The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are $\sqrt{np},np\left ( 1-2p \right )$ $\sqrt{np},\sqrt{np\left ( 1-p \right )}$ $np,np$ $np, np\left ( 1-p \right )$
ShouvikSVK
answered
in
Probability and Statistics
Jan 22
by
ShouvikSVK
280
points
gateme-2021-set2
probability-and-statistics
probability
binomial-distribution
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 8
A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critical path is $3$ $9$ $27$ $81$
go_editor
asked
in
Probability and Statistics
Mar 1, 2021
by
go_editor
5.0k
points
gateme-2021-set2
probability-and-statistics
statistics
mode-and-standard-deviation
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 5
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as Exponential Bernoulli Binomial Normal
gatecse
asked
in
Probability and Statistics
Feb 22, 2021
by
gatecse
1.6k
points
gateme-2021-set1
probability-and-statistics
probability
random-variables
normal-distribution
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 33
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes after the shop opens. The probability that a customer arrives within the next $3$ minutes is $0.39$ $0.86$ $0.50$ $0.61$
gatecse
asked
in
Probability and Statistics
Feb 22, 2021
by
gatecse
1.6k
points
gateme-2021-set1
probability-and-statistics
probability
poisson-distribution
1
answer
0
votes
GATE2020-ME-2: 36
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in the next ten tosses is _________ (round off to $3$ decimal places)
haralk10
answered
in
Probability and Statistics
Dec 29, 2020
by
haralk10
180
points
gateme-2020-set2
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE2020-ME-2: 1
The sum of two normally distributed random variables $X$ and $Y$ is always normally distributed normally distributed, only if $X$ and $Y$ are independent normally distributed, only if $X$ and $Y$ have the same standard deviation normally distributed, only if $X$ and $Y$ have the same mean
go_editor
asked
in
Probability and Statistics
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
probability-and-statistics
probability
normal-distribution
1
answer
0
votes
GATE Mechanical 2014 Set 1 | Question: 28
In the following table, $x$ is a discrete random variable and $p(x)$ is the probability density. The standard deviation of $x$ is $\begin{array}{|c|c|c|c|} \hline x & 1 & 2 & 3 \\ \hline p(x) & 0.3 & 0.6 & 0.1 \\ \hline \end{array}$ $0.18$ $0.36$ $0.54$ $0.60$
Gyanu
answered
in
Probability and Statistics
Sep 3, 2020
by
Gyanu
140
points
gateme-2014-set1
probability-and-statistics
probability
random-variables
mode-and-standard-deviation
1
answer
0
votes
GATE2019 ME-2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
Shalini26
answered
in
Probability and Statistics
May 18, 2019
by
Shalini26
160
points
gateme-2019-set2
numerical-answers
probability-and-statistics
statistics
0
answers
0
votes
GATE2019 ME-2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).
Arjun
asked
in
Probability and Statistics
Feb 9, 2019
by
Arjun
27.4k
points
gateme-2019-set2
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE2019 ME-1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
Arjun
asked
in
Probability and Statistics
Feb 9, 2019
by
Arjun
27.4k
points
gateme-2019-set1
probability-and-statistics
probability
uniform-distribution
0
answers
0
votes
GATE ME 2012 | Question: 45
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is $1/20$ $1/12$ $3/10$ $1/2$
Andrijana3306
asked
in
Probability and Statistics
Mar 20, 2018
by
Andrijana3306
1.5k
points
gateme-2012
probability-and-statistics
probability
1
answer
0
votes
GATE2018-2-24
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between successive customer arrival is between $1$ and $3$ minutes is _____ (correct to two decimal places)
Balaji Jegan
answered
in
Probability and Statistics
Feb 22, 2018
by
Balaji Jegan
1.2k
points
gateme-2018-set2
numerical-answers
probability-and-statistics
probability
poisson-distribution
1
answer
0
votes
GATE2018-2-27
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$
Balaji Jegan
answered
in
Probability and Statistics
Feb 22, 2018
by
Balaji Jegan
1.2k
points
gateme-2018-set2
probability-and-statistics
probability
random-variables
exponential-distributions
0
answers
0
votes
GATE2018-1-26
Let $X_1, \: X_2$ be two independent normal random variables with means $\mu_1, \: \ \mu_2$ and standard deviations $\sigma_1, \: \sigma_2$, respectively. Consider $Y=X_1-X_2; \: \mu_1 = \mu_2 =1, \: \sigma_1=1, \: \sigma_2=2$. Then, $Y$ is normally ... $0$ and variance $5$, but is NOT normally distributed $Y$ has mean $0$ and variance $1$, but is NOT normally distributed
Arjun
asked
in
Probability and Statistics
Feb 17, 2018
by
Arjun
27.4k
points
gateme-2018-set1
probability-and-statistics
probability
random-variables
mode-and-standard-deviation
0
answers
0
votes
GATE2018-1-18
A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is $33.3$ $3.33$ $0.33$ $0.0033$
Arjun
asked
in
Probability and Statistics
Feb 17, 2018
by
Arjun
27.4k
points
gateme-2018-set1
probability-and-statistics
probability
0
answers
0
votes
GATE2018-1-1
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is $1/72$ $1/55$ $1/36$ $1/27$
Arjun
asked
in
Probability and Statistics
Feb 17, 2018
by
Arjun
27.4k
points
gateme-2018-set1
probability-and-statistics
probability
0
answers
0
votes
GATE2017 ME-2: 24
The standard deviation of linear dimensions $P$ and $Q$ are $3 \mu$ m and $4 \mu$ m, respectively. When assembled, the standard deviation (in $\mu$ m) of the resulting linear dimension $(P+Q)$ is _________.
Arjun
asked
in
Probability and Statistics
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set2
numerical-answers
probability-and-statistics
mode-and-standard-deviation
0
answers
0
votes
GATE2017 ME-2: 1
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.
Arjun
asked
in
Probability and Statistics
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set2
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE2017 ME-2: 4
A sample of $15$ data is as follows: $17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3$. The mode of the data is $4$ $13$ $17$ $20$
Arjun
asked
in
Probability and Statistics
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set2
probability-and-statistics
statistics
mode-and-standard-deviation
0
answers
0
votes
GATE2017 ME-1: 5
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.
Arjun
asked
in
Probability and Statistics
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set1
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE2016-3-29
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\dfrac{16}{5525} \\$ $\dfrac{64}{2197} \\$ $\dfrac{3}{13} \\$ $\dfrac{8}{16575}$
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set3
probability-and-statistics
probability
0
answers
0
votes
GATE2016-3-4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set3
numerical-answers
probability-and-statistics
probability
normal-distribution
0
answers
0
votes
GATE2016-2-28
The probability that a screw manufactured by a company is defective is $0.1$. The company sells screws in packets containing $5$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set2
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE2016-1-4
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $μ$. The standard deviation for this distribution is given by $\sqrt{\mu }$ $\mu ^2$ $\mu$ $1/\mu$
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set1
probability-and-statistics
probability
poisson-distribution
mode-and-standard-deviation
0
answers
0
votes
GATE2015-3-14
If $P(X) = \displaystyle{\frac{1}{4}}$, $P(Y) = \displaystyle{\frac{1}{3}}$, and $P(X \cap Y) = \displaystyle{\frac{1}{12}}$, the value of $P(Y/X)$ is $\displaystyle{\frac{1}{4}} \\$ $\displaystyle{\frac{4}{25}} \\$ $\displaystyle{\frac{1}{3}} \\$ $\displaystyle{\frac{29}{50}}$
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2015-set3
probability-and-statistics
probability
conditional-probability
0
answers
0
votes
GATE2015-2-26
The chance of a student passing an exam is $20 \%$. The chance of a student passing the exam and getting above $90 \%$ marks in it is $5 \%$. GIVEN that a student passes the examination, the probability that the student gets above $90 \%$ marks is $\dfrac{1}{18} \\ $ $\dfrac{1}{4} \\$ $\dfrac{2}{9} \\$ $\dfrac{5}{18}$
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2015-set2
probability-and-statistics
probability
0
answers
0
votes
GATE2015-1-29
The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is $425/432$ $19/144$ $13/144$ $125/432$
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2015-set1
probability-and-statistics
probability
0
answers
0
votes
GATE2015-1-2
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? $I$ $II$ $III$ $IV$
Arjun
asked
in
Probability and Statistics
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2015-set1
probability-and-statistics
probability
normal-distribution
variance
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 28
The number of accidents occurring in a plant in a month follows Poisson distribution with mean as $5.2$. The probability of occurrence of less than $2$ accidents in the plant during a randomly selected month is $0.029$ $0.034$ $0.039$ $0.044$
Arjun
asked
in
Probability and Statistics
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set4
probability-and-statistics
probability
poisson-distribution
0
answers
0
votes
GATE Mechanical 2014 Set 3 | Question: 4
A group consists of equal number of men and women. Of this group $20$% of the men and $50$% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______
Arjun
asked
in
Probability and Statistics
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set3
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 28
Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _______
Arjun
asked
in
Probability and Statistics
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set2
numerical-answers
probability-and-statistics
probability
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 4
A box contains $25$ parts of which $10$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is $\dfrac{7}{20} \\$ $\dfrac{42}{125} \\$ $\dfrac{25}{29} \\$ $\dfrac{5}{9}$
Arjun
asked
in
Probability and Statistics
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set2
probability-and-statistics
probability
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 50
Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the ... be $\dfrac{5}{7} \\$ $\dfrac{14}{3} \\$ $\dfrac{7}{5} \\$ $\dfrac{10}{3}$
Arjun
asked
in
Probability and Statistics
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set1
probability-and-statistics
probability
poisson-distribution
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 18
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is Normal Poisson Erlang Beta
Arjun
asked
in
Probability and Statistics
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set1
probability-and-statistics
probability
poisson-distribution
0
answers
0
votes
GATE ME 2013 | Question: 45
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has ... answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
piyag476
asked
in
Probability and Statistics
Feb 19, 2017
by
piyag476
1.4k
points
gateme-2013
probability-and-statistics
probability
conditional-probability
0
answers
0
votes
GATE ME 2013 | Question: 24
Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$ is $0.5$ greater than zero and less than $0.5$ greater than $0.5$ and less than $1.0$ $1.0$
piyag476
asked
in
Probability and Statistics
Feb 19, 2017
by
piyag476
1.4k
points
gateme-2013
probability-and-statistics
probability
random-variables
variance
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