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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 $\sqrt{np},np\left ( 1-2p \right )$ $\sqrt{np},\sqrt{np\left ( 1-p \right )}$ $np,np$ $np, np\left ( 1-p \right )$
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 )$$...
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GATE2020-ME-2: 36
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in the next ten tosses is _________ (round off to $3$ decimal places)
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in t...
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GATE2019 ME-2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
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GATE2018-1-18
A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is $33.3$ $3.33$ $0.33$ $0.0033$
A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is$33.3$$3.33$$0.33$$0.0033$
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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 $1/72$ $1/55$ $1/36$ $1/27$
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 probabil...
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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 $1/6$
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ isexponentially...
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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)
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 s...
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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 $4$ $13$ $17$ $20$
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$$20$
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GATE2017 ME-2: 1
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.
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GATE2017 ME-1: 5
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.
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GATE2016-3-29
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\dfrac{16}{5525} \\$ $\dfrac{64}{2197} \\$ $\dfrac{3}{13} \\$ $\dfrac{8}{16575}$
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is$\dfrac{16}{5525} \\$$\dfrac{64}{2197} \\$$\dfrac{3}{13} \\$...
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GATE2016-3-4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
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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 $\sqrt{\mu }$ $\mu ^2$ $\mu$ $1/\mu$
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{\...
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GATE2015-1-29
The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is $425/432$ $19/144$ $13/144$ $125/432$
The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is$425/432$$19/144$$13/144$$125/432$
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GATE2015-1-2
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? $I$ $II$ $III$ $IV$
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?$I$$II$$III$$IV$
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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 $\begin{array}{|c|c|c|c|} \hline x & 1 & 2 & 3 \\ \hline p(x) & 0.3 & 0.6 & 0.1 \\ \hline \end{array}$ $0.18$ $0.36$ $0.54$ $0.60$
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 &...
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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
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 isNormalPoissonErlangB...
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