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Syllabus: Random variables, Uniform, Normal, Exponential, Poisson and Binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 0 &1&1&0&2&1&1&0&1&1&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&2&1&1&1&0&3&1&0&0&1.1&3
\\\hline\textbf{Total Marks} & 0 &5&5&2&4&3&1&6&3&1&\bf{0}&\bf{3}&\bf{6}\\\hline
\end{array}}}$$

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2 votes
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261
NIELIT 2016 MAR Scientist B - Section B: 17
Following marks are obtained by the students in a test: $81,72,90,90,86,85,92,70,71,83,89,95,85,79,62$. Range of the marks is $9$ $17$ $27$ $33$
Following marks are obtained by the students in a test:$81,72,90,90,86,85,92,70,71,83,89,95,85,79,62$. Range of the marks is$9$$17$$27$$33$
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2 votes
2 answers
262
UGC NET CSE | August 2016 | Part 3 | Question: 54
An experimental file server is up $75$% of the time and down for $25$% of the time due to bugs. How many times does this file server have to be replicated to give an availability of at least $99$% ? $2$ $4$ $8$ $16$
An experimental file server is up $75$% of the time and down for $25$% of the time due to bugs. How many times does this file server have to be replicated to give an avai...
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2 votes
2 answers
267
ISI2016-MMA-9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ?$\lambda$$2 \lambd...
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14 votes
2 answers
270
TIFR CSE 2010 | Part A | Question: 6
Given 10 tosses of a coin with probability of head = .$4$ = ($1$ - the probability of tail), the probability of at least one head is? $(.4)^{10}$ $1 - (.4)^{10}$ $1 - (.6)^{10}$ $(.6)^{10}$ $10(.4) (.6)^{9}$
Given 10 tosses of a coin with probability of head = .$4$ = ($1$ - the probability of tail), the probability of at least one head is?$(.4)^{10}$$1 - (.4)^{10}$$1 - (.6)^{...
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0 votes
3 answers
275
UGC NET CSE | July 2018 | Part 2 | Question: 80
Consider the set of all possible five-card poker hands dealt fairly from a standard deck of fifty-two cards. How many atomic events are there in the joint probability distribution? 2, 598, 960 3, 468, 960 3, 958, 590 2, 645, 590
Consider the set of all possible five-card poker hands dealt fairly from a standard deck of fifty-two cards. How many atomic events are there in the joint probability dis...
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1 votes
2 answers
276
NIELIT DEC 2017 SET-C 62
If a random coin is tossed 11 times then what is the probability that for 7th toss head appears exactly 4 times? 5/32 15/128 35/128 None of the options
If a random coin is tossed 11 times then what is the probability that for 7th toss head appears exactly 4 times?5/3215/12835/128None of the options
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3 votes
1 answer
278
ISI2015-MMA-51
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n-1}$ $\frac{1}{n-2}$
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals$\frac{1}{n}$$\frac{2}{n}$$\frac{1}{n-1}...
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4 votes
3 answers
279
ISRO2014-74
What is the median of data if its mode is $15$ and the mean is $30?$ $30$ $25$ $22.5$ $27.5$
What is the median of data if its mode is $15$ and the mean is $30?$$30$$25$$22.5$$27.5$
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2 votes
1 answer
280
GATE 2015 SET-2 Q 29
Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______.
Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _____...
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