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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

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

Previous GATE Questions in Probability

35 votes
6 answers
32
20 votes
2 answers
33
27 votes
4 answers
37
35 votes
5 answers
38
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of ...
36 votes
4 answers
39
The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .
39 votes
5 answers
42
Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $\dfrac{X}{1296}$. The value of $X$ is _______
61 votes
3 answers
44
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
30 votes
8 answers
46
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is$\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}...
41 votes
4 answers
47
Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and ...
61 votes
6 answers
48
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 ...