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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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} &\textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &2&1&0& 0 &1&1&0&0.83&2
\\\hline\textbf{2 Marks Count} & 1&1&1&0 &2&2&0&1.16&2
\\\hline\textbf{Total Marks} & 4&3&2&0 &5&5&\bf{0}&\bf{3.16}&\bf{5}\\\hline
\end{array}}}$$

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GATE DS&AI 2024 | Question: 2
​​​​​Three fair coins are tossed independently. $T$ is the event that two or more tosses result in heads. $S$ is the event that two or more tosses result in tails. What is the probability of the event $T \cap S$? $0$ $0.5$ $0.25$ $1$
​​​​​Three fair coins are tossed independently. $T$ is the event that two or more tosses result in heads. $S$ is the event that two or more tosses result in tai...
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6
GATE DS&AI 2024 | Question: 26
​​​​​A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$
​​​​​A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently.What is the expected number of times the die is thrown until t...
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10
GATE CSE 2024 | Set 2 | Question: 8
​​​​​​When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers $(i.e., 1, 2, 3, 4, 5, \text{and } 6)$ is $\frac{1}{324}$ $\frac{5}{324}$ $\frac{7}{324}$ $\frac{11}{324}$
​​​​​​When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers $(i.e., 1, 2, 3, 4, 5, \text{and } 6)$ is$\frac{1}{3...
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17
Memory Based GATE DA 2024 | Question: 1
Consider the probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\) and \(\lambda > 0\). Determine the value of \(\lambda\) such that \(5E(x) = V(x)\).
Consider the probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\) and \(\lambda 0\). Determine the value of \(\lambda\) such that \(5E(x) = V(...
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Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}{\sigma}\).
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}...
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