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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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probability
Consider a hash table with 10 slots. Collisions are resolved using linear probing. The probability that if first 3 slots are unfilled and 4th insertions leads to a collisions ________. (Upto 3 decimal places) // my answer is 7/10 * 6/10 * 5/10 * 3/7 = 90/1000 = 0.09
Consider a hash table with 10 slots. Collisions are resolved using linear probing. The probability that if first 3 slots are unfilled and 4th insertions leads to a collis...
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454
Probability- Gravner - 23
Roll a die $12$ times. Compute the probability that a number occurs $6$ times and two other numbers occur three times each.
Roll a die $12$ times. Compute the probability that a number occurs $6$ times and two other numbers occur three times each.
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455
Conditional Probability
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TANCET 2011 PROBABILITY
A man alternately tosses a coin and throws a dice, beginning with the coin. Then probability that he will get a head before he gets a 5 or 6 on dice is 1) 1/4 2) 3/4 3) 4/5 4) 4/7
A man alternately tosses a coin and throws a dice, beginning with the coin. Then probability that he will get a head before he gets a 5 or 6 on dice is1) 1/42) 3/43) 4/54...
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457
Probability- Gravner- 76
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
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458
Self doubt
1) P(A/B) = P(A $\cap$ B) / P(B) 2) P(A/B) = P(B $\cap$ A) / P(B) What is the difference in this equation.. P(A $\cap$ B) and P(B $\cap$​​​​​​​ A) are same ???
1) P(A/B) = P(A $\cap$ B) / P(B)2) P(A/B) = P(B $\cap$ A) / P(B)What is the difference in this equation..P(A $\cap$ B) and P(B $\cap$​​​​​​​ A) are same ??...
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460
#made easy test
A pair of dice rolled together till a sum of either 5 or 7 obtained. find probability that 5 comes before 7.
A pair of dice rolled together till a sum of either 5 or 7 obtained. find probability that 5 comes before 7.
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461
Probability
From a deck of 52 cards, what is the probability of picking 2 kings: a)With replacement B)Without replacement Please explain in details. I am new to probability. Thank you. :)
From a deck of 52 cards, what is the probability of picking 2 kings:a)With replacementB)Without replacement Please explain in details. I am new to probability. Thank you....
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462
Probability Doubt
What is the difference between Independent Events and Disjoint Events?
What is the difference between Independent Events and Disjoint Events?
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463
ME Test Series
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464
#MADE ESAY
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465
Birthday Paradox
In a room of $23$ people what is the probability that $2$ of. them has a birthday in common?
In a room of $23$ people what is the probability that $2$ of. them has a birthday in common?
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466
Random Variables
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467
engg math book
out of 800 families with 5 children each,how many families would be expected to have 1. 3boy 2. 2girls
out of 800 families with 5 children each,how many families would be expected to have1. 3boy 2. 2girls
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468
Probability- Gravner- 82.b
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (b) Write down an approximation, in terms on $n$ and $\phi$, of the probability that $M$ differs from its expectation by less than $10$ %
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large.(b) Write down an approximation, in terms on $n$ and $\phi$, of the probabi...
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469
Probability - Gravner-73
Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, compute the probability that it lasts more than $200$ hours and the probability that it lasts less than $50$ hours.
Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, compute the probability that it lasts more than $200$ hours and the probability ...
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Probability - Gravner-33.a
An urn contains 10 black and 10 white balls. Draw 3 a) without replacement
An urn contains 10 black and 10 white balls. Draw 3a) without replacement
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