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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

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

Most answered questions in Probability

47 votes
4 answers
61
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
1 votes
4 answers
63
What is the probability of choosing correctly an unknown integer between $0$ and $9$ with $3$ chances ?$\frac{963}{1000}$$\frac{973}{1000}$$\frac{983}{1000}$$\frac{953}{1...
1 votes
4 answers
64
If the proposition $\neg P \to Q$ is true, then the truth value of the proposition $\neg P \vee ( P \to Q)$ isTrue Multi-valued False Can no...
6 votes
4 answers
65
A fair coin is tossed 3 times in succession.If the first toss produced a head then the probability of getting exactly two heads in 3 tosses(including the first toss ) is1...
6 votes
4 answers
66
Three coins are tossed simultaneously. The probability that they will fall two heads and one tail is$5/8$$1/8$$2/3$$3/8$
2 votes
4 answers
68
Probability of getting a total of 7 atleast once in three toss of a fair die is125/21691/216117/2169/216
19 votes
4 answers
69
Assume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the expected number of coin flips required to obtain two consecutive heads for...
14 votes
4 answers
70
The probability of three consecutive heads in four tosses of a fair coin is$\left(\dfrac{1}{4}\right)$$\left(\dfrac{1}{8}\right)$$\left(\dfrac{1}{16}\right)$$\left(\dfrac...
3 votes
4 answers
71
X is uniformly distributed random variable that takes values between 0 and 1.The value of E(X^3) will be
4 votes
4 answers
73
What is the probability that a five-card poker hand contains a straight, that is, five cards that have consecutive kinds?Answer is 10240/C(52,5)My approch:2*(4)^5/C(52,5)...
23 votes
4 answers
77
The probability that top and bottom cards of a randomly shuffled deck are both aces is$\frac{4}{52} \times \frac{4}{52}$$\frac{4}{52} \times \frac{3}{52}$$\frac{4}{52} \t...
27 votes
4 answers
79
36 votes
4 answers
80
The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .