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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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Recent questions in Probability

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281
Probability_#52
Consider the following probability mass function of a random variable X $p(X,q)=\{q\,\,if\,X=0 \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1-q\,\,\,if\,X=1\\ 0\,\,otherwise$ If q=0.4, the variance of X is.?
Consider the following probability mass function of a random variable X$p(X,q)=\{q\,\,if\,X=0 \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1-q\,\,\,if\,X=1\\...
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282
Made easy workbook
Suppose the random variable X has the probability distribution given below: X -2 -1 0 1 2 P(X=X) 0.25 0.20 0.15 0.35 0.05 Let $Y=(2*(X^2))+6$.The expected value E(Y) is: A) 9.5 B) 6. C )15.5. D )18
Suppose the random variable X has the probability distribution given below:X-2-1012P(X=X)0.250.200.150.350.05Let $Y=(2*(X^2))+6$.The expected value E(Y) is:A) 9.5 B) ...
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284
Sheldon ross 5J
A deck of 52 playing cards is shuffled, and the cards are turned up one at a time until the first ace appears. Is the next card—that is, the card following the first ace—more likely to be the ace of spades or the two of clubs?
A deck of 52 playing cards is shuffled, and the cards are turned up one at a time untilthe first ace appears. Is the next card—that is, the card following the first ace...
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285
Sheldon Ross 5i
There are 50 people in the room, the probability that at least two share the same birthday is approximately( Consider the ordinary year)......?
There are 50 people in the room, the probability that at least two share thesame birthday is approximately( Consider the ordinary year)......?
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286
Sheldon Ross example 5h
In the game of bridge, the entire deck of 52 cards is dealt out to 4 players. What is the probability that (a) one of the players receives all 13 spades; (b) each player receives 1 ace?
In the game of bridge, the entire deck of 52 cards is dealt out to 4 players. What is theprobability that(a) one of the players receives all 13 spades;(b) each player rec...
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287
#Sheldon ross example
suppose 5 people are to be randomly selected from a group of 20 individuals consisting of 10 married couples, and we want to determine P(N), the probability that the 5 chosen are all unrelated. (That is, no two are married to each other.)?
suppose 5 people are to be randomly selected from a group of 20 individualsconsisting of 10 married couples, and we want to determine P(N), the probabilitythat the 5 chos...
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288
possible solutions
How many distinct solutions does the following equation have? $x _ { 1 } + x _ { 2 } + x _ { 3 } + x _ { 4 } = 100 $$x _ { 1 } \in \{ 1,2,3 . . \} , x _ { 2 } \in \{ 2,3,4 , \ldots \} , x _ { 3 } , x _ { 4 } \in \{ 0,1,2,3 , \dots \} $
How many distinct solutions does the following equation have?$$x _ { 1 } + x _ { 2 } + x _ { 3 } + x _ { 4 } = 100 $$$x _ { 1 } \in \{ 1,2,3 . . \} , x _ { 2 } \in \{ 2,3...
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290
ACE Test series question
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291
ACE TEST SERIES QUESTION
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292
Basic Probability
A person throwing a dice and when even have come he got $2$ points and when odd have come he got $1$ points.What is the probability when he got exactly $6$ points?
A person throwing a dice and when even have come he got $2$ points and when odd have come he got $1$ points.What is the probability when he got exactly $6$ points?
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293
ACE TEST SERIES QUESTION
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294
Mathematics: GATE-ME-2018
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295
Mathematics: GATE-ME-2018
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296
Consider an undirected random graph of eight vertices.
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\large \frac{1}{2}$. What is the probability that graph contains exactly 2 cycles of length 3?
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\large \frac{1}{2}$. What is the probability t...
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297
PROBABILITY
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298
PROBABILITY
HOW TO DECIDE OR CHECK??
HOW TO DECIDE OR CHECK??
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299
PROBABILTY
A POINT P IS CHOOSEN AT RANDOM ON A LINE AB OF LENGTH 2L .THE PROBABILTY P[(AP*BP)>L^2/2] IS ...... AND ALSO SUGGEST THAT THESE KIND OF QUESTION ON PROBABILTY CAN ARRISE IN EXAM FOR CS BRANCH??
A POINT P IS CHOOSEN AT RANDOM ON A LINE AB OF LENGTH 2L .THE PROBABILTYP[(AP*BP)>L^2/2] IS ......AND ALSO SUGGEST THAT THESE KIND OF QUESTION ON PROBABILTY CAN ARRISE IN...
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300
Random Variables
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