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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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Most viewed questions in Probability

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391
Random Variable
Let X and Y are two random variables with E(X)=10,E(Y)=20 and Var(X)=25,Var(Y)=36 and E(X.Y)=225. Now consider Z=aX-bY+1. Find a and b when E(Z)=1 and Var(Z)=1.
Let X and Y are two random variables with E(X)=10,E(Y)=20 and Var(X)=25,Var(Y)=36 and E(X.Y)=225.Now consider Z=aX-bY+1.Find a and b when E(Z)=1 and Var(Z)=1.
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1 votes
2 answers
392
NIELIT 2017 DEC Scientific Assistant A - Section B: 41
If a random coin is tossed $11$ times, then what is the probability that for $7$th toss head appears exactly $4$ times? $5/32$ $15/128$ $35/128$ None of the options
If a random coin is tossed $11$ times, then what is the probability that for $7$th toss head appears exactly $4$ times?$5/32$$15/128$$35/128$None of the options
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394
1.You are in a game show! There are 10 closed doors, 0 leads to nothing and 1 leads to an expensive sports car.
Q.You are in a game show! There are 10 closed doors, 0 leads to nothing and 1 leads to an expensive sports car. You are allowed to pick a door and earn the sports car if ...
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397
Expectation
Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. What is the expected number of people to get their own hat back. Hint: express the number of people who get their own hat as a sum of random variables whose expected value is easy to compute.
Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. What is the expected number of people to get their own hat back.Hint: express th...
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0 votes
3 answers
399
ISRO 2014- Probability [Mech]
A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin? a) 70/82 b) 35/70 c) 41/82 d) 41/70
A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. W...
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2 votes
1 answer
400
Standard Deviation
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1 votes
1 answer
402
GATE DS&AI 2024 | Question: 26
​​​​​A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$
​​​​​A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently.What is the expected number of times the die is thrown until t...
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5 votes
1 answer
403
Probability
In a boxing tournament 2n equally skilled players P1,P2,P3...........P$2^{n}$ ... $\frac{3}{4} * \frac{1}{2^{n}-1}$ D. $\frac{7}{8} * \frac{1}{2^{n}-1}$
In a boxing tournament 2n equally skilled players P1,P2,P3...........P$2^{n}$, are participating.In each round players are divided in pairs at random and winner from each...
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2 votes
3 answers
405
NIELIT 2016 MAR Scientist B - Section B: 16
A box contains $10$ screws, $3$ of which are defective. Two screws are drawn at random with replacement. The probability that none of two screws is defective will be $100\%$ $50\%$ $49\%$ None of these.
A box contains $10$ screws, $3$ of which are defective. Two screws are drawn at random with replacement. The probability that none of two screws is defective will be$100\...
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