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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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Highest voted questions in Probability

73 votes
8 answers
3
GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is$3...
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61 votes
3 answers
5
GATE CSE 2014 Set 1 | Question: 2
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
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61 votes
6 answers
6
GATE CSE 2013 | Question: 24
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\dfrac{1}{2}.$ What is the expected number of unordered cycles of length three? $\dfrac {1}{8}$ $1$ $7$ $8$
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\dfrac{1}{2}.$ What is the expected number of ...
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56 votes
3 answers
7
GATE CSE 2010 | Question: 27
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$?$\left(\dfrac{1}{625}\right)$$\left(\dfrac{4}{625}\right)$$\left(\dfrac{12}{625}\right)$$\lef...
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48 votes
5 answers
13
GATE CSE 2017 Set 1 | Question: 19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ ...
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47 votes
4 answers
15
GATE CSE 2017 Set 2 | Question: 48
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
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