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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

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

Recent questions in Probability

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373
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(d) Find an expression for $P(Y>10)$.
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374
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(c) Find an expression $P$($X\geqslant 6$)...
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375
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(b) Write down the probability mass functi...
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376
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(a) Write down the probability mass functi...
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377
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379
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.