Register

Web Page

Syllabus: Random variables, Uniform, Normal, Exponential, Poisson and Binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem

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

Filter

Recent questions in Probability

0 votes
0 answers
421
Probability - Gravner-63
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the game repeats. On the average, how many rounds does the game last?
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the ...
User Avatar
0 votes
0 answers
423
Probability - Gravner-61
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
User Avatar
0 votes
0 answers
425
Probability - Gravner-59
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
User Avatar
0 votes
1 answer
426
Probablity-Gravner-58
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
User Avatar
0 votes
1 answer
427
Probability - Gravner-56
Let $X$ be a random variable with $P(X=1) =0.2, P(X=2) = 0.3$, and $P(X=3) = 0.5$. What is the expected value of $X$?
Let $X$ be a random variable with $P(X=1) =0.2, P(X=2) = 0.3$, and $P(X=3) = 0.5$. What is the expected value of $X$?
User Avatar
0 votes
1 answer
429
Probability - Gravner-55
An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f. and the probability that at least one the selected numbers is $15$ or more.
An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f...
User Avatar
0 votes
1 answer
430
Probability - Gravner-54
Let $X$ be the number of Heads in $2$ fair coin tosses. Determine its p.m.f.
Let $X$ be the number of Heads in $2$ fair coin tosses. Determine its p.m.f.
User Avatar
0 votes
0 answers
433
Probability - Gravner-52.b
Five married couples are seated at random around a round table. (b) Compute the probability that at most one wife does not sit next to her husband.
Five married couples are seated at random around a round table.(b) Compute the probability that at most one wife does not sit next to her husband.
User Avatar
0 votes
0 answers
434
Probability - Gravner-52.a
Five married couples are seated at random around a round table. (a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent seats).
Five married couples are seated at random around a round table.(a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent s...
User Avatar
0 votes
0 answers
435
Probability - Gravner-51.b
Ten fair dice are rolled. What is the probability that: (b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.
Ten fair dice are rolled. What is the probability that:(b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.
User Avatar
0 votes
1 answer
436
Probability - Gravner-51.a
Ten fair dice are rolled. What is the probability that: a) At least one $1$ appears.
Ten fair dice are rolled. What is the probability that:a) At least one $1$ appears.
User Avatar
0 votes
0 answers
437
Probability - Gravner-51.c
Ten fair dice are rolled. What is the probability that: (c) Each of the number $1,2,3$ appears at least once.
Ten fair dice are rolled. What is the probability that:(c) Each of the number $1,2,3$ appears at least once.
User Avatar
Page: