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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

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

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Recent questions in Probability

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571
Probability Density Function
Given a probability density function $\frac{1}{x}$. Value exists in the interval $\left ( 2,3 \right )$ Can this pdf has existence outside this range?
Given a probability density function $\frac{1}{x}$. Value exists in the interval $\left ( 2,3 \right )$Can this pdf has existence outside this range?
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576
IIT M Written : Probability
An experiment is performed $n$ times, in each of which an event $X$ may occur with a probability $p$. Determine$ E[ \overline{X}]$ and $Var( \overline{X})$, where $\overline{X} $is the complement of the event $X$
An experiment is performed $n$ times, in each of which an event $X$ may occur with a probability $p$. Determine$ E[ \overline{X}]$ and $Var( \overline{X})$, where $\overl...
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577
IIT M Written Test
Any Hints on how to solve this?
Any Hints on how to solve this?
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1 votes
2 answers
579
Doubt
Suppose we are playing a game.You have to choose 1 out 3 doors.Behind 1 lucky door ,we have 1 million dollars.You picked 1 st door.But i opened the 3rd door and found nothing.Now,if i give you another chance ,will you change your choice? (Use probabiliy estimates to answer)
Suppose we are playing a game.You have to choose 1 out 3 doors.Behind 1 lucky door ,we have 1 million dollars.You picked 1 st door.But i opened the 3rd door and found not...
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1 votes
2 answers
580
Bayes theorem
This is extended form of Bayes theorem Can somebody explain (or can prove), how from 1st line 2 line came?
This is extended form of Bayes theoremCan somebody explain (or can prove), how from 1st line 2 line came?
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581
Intermediate Conting and Probability
Solve
Solve
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1 answer
582
Intermediate Conting and Probability(David Patrick)
Solve
Solve
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2 votes
1 answer
583
IISc CDS(MTech -R)
There are 12 pair of shoes, what is the probability that atleast one complete pair of shoes are present if 4 shoes are selected at random?
There are 12 pair of shoes, what is the probability that atleast one complete pair of shoes are present if 4 shoes are selected at random?
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587
Probability
Prove for a positive integer valued random variable, $X$ , and for positive integers $a < b$ \begin{align*} &P(X \geq b) \leq \left [ \left ( \frac{E(X)}{b} \right ) - P(a \leq X < b)\cdot \left ( \frac{a}{b} \right ) \right ] \\ \end{align*}
Prove for a positive integer valued random variable, $X$ , and for positive integers $a < b$\begin{align*} &P(X \geq b) \leq \left [ \left ( \frac{E(X)}{b} \right ) - P(...
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588
isi_kolkata
E1 and E2 are two events such that P(E1) = 0.2 and P(E2) = 0.5. What are the minimum and maximum possible values of P(E1c | E2c)? (A) 0 and 0.6 (B) 0.4 and 0.6 (C) 0.4 and 1 (D) 0.6 and 1
E1 and E2 are two events such that P(E1) = 0.2 and P(E2) = 0.5.What are the minimum and maximum possible values of P(E1c | E2c)?(A) 0 and 0.6 (B) 0.4 and 0.6 (C) 0.4 and ...
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5 votes
3 answers
590
ISRO2018-14
A class of $30$ students occupy a classroom containing $5$ rows of seats, with $8$ seats in each row. If the students seat themselves at random, the probability that sixth seat in the fifth row will be empty is: $1/5$ $1/3$ $1/4$ $2/5$
A class of $30$ students occupy a classroom containing $5$ rows of seats, with $8$ seats in each row. If the students seat themselves at random, the probability that sixt...
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