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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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102
TIFR
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105
GATE CSE 2014 Set 1 | Question: 48
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 _______
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 _______
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1 votes
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106
DRDO CSE 2022 Paper 1 | Question: 5 (b)
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets representing the following events. $\mathrm{A}$ and $\mathrm{B}$
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets repre...
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107
DRDO CSE 2022 Paper 1 | Question: 5 (c)
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets representing the following events. not $\text{B}$
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets repre...
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109
canvas
The weight of a light bulb has an average of 12.5 grs. with a standard deviation of 2. Assume the variable is normally distributed. If an inspector select randomly a sample of 30 bulbs ¿what is the probability of the weight of one bulb falls between 10 and 15 grs.?
The weight of a light bulb has an average of 12.5 grs. with a standard deviation of 2. Assume the variable is normally distributed. If an inspector select randomly a sa...
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3 votes
4 answers
113
Uniform probability distribution
X is uniformly distributed random variable that takes values between 0 and 1.The value of E(X^3) will be
X is uniformly distributed random variable that takes values between 0 and 1.The value of E(X^3) will be
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115
TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\righ...
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116
Test series
A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is 1/2 3/5 1/4 4/6
A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is 1/2 3/5 1/4 4/6
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118
Variance of X in envelope question
Three letters are placed into three addressed envelopes randomly. A random variable X denotes the number of letters placed into corresponding envelopes. The variance of X is __________.
Three letters are placed into three addressed envelopes randomly. A random variable X denotes the number of letters placed into corresponding envelopes. The variance of X...
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