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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

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

Recent questions in Probability

0 votes
1 answer
1
If $A$ and $B$ are two related events, and $P(A \mid B)$ represents the conditional probability, Bayes’ theorem states that $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$
asked Apr 2 in Probability Lakshman Patel RJIT 101 views
0 votes
2 answers
2
1 vote
2 answers
3
1 vote
2 answers
4
If $X, Y$ and $Z$ are three exhaustive and mutually exclusive events related with any experiment and the $P\left(X \right)=0.5P\left(Y \right)$ and $P\left(Z \right)$ = $0.3P\left(Y \right)$. Then $P\left(Y \right)$ = ___________ . $0.54$ $0.66$ $0.33$ $0.44$
asked Mar 31 in Probability Lakshman Patel RJIT 415 views
0 votes
2 answers
5
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.
asked Mar 31 in Probability Lakshman Patel RJIT 237 views
0 votes
1 answer
6
Following marks are obtained by the students in a test: $81,72,90,90,86,85,92,70,71,83,89,95,85,79,62$. Range of the marks is $9$ $17$ $27$ $33$
asked Mar 31 in Probability Lakshman Patel RJIT 102 views
1 vote
1 answer
7
1 vote
1 answer
8
A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls are red and two are green ? $\large\frac{3}{7}$ $\large\frac{4}{7}$ $\large\frac{5}{7}$ $\large\frac{6}{7}$
asked Mar 28 in Probability jothee 177 views
6 votes
4 answers
9
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.
asked Feb 12 in Probability Arjun 2.3k views
2 votes
1 answer
10
Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above
asked Feb 11 in Probability Lakshman Patel RJIT 138 views
0 votes
2 answers
11
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
asked Feb 10 in Probability Lakshman Patel RJIT 334 views
1 vote
2 answers
12
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent of the other winners. ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
asked Feb 10 in Probability Lakshman Patel RJIT 230 views
0 votes
0 answers
13
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it moves to one ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
asked Feb 10 in Probability Lakshman Patel RJIT 107 views
1 vote
2 answers
14
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
asked Feb 10 in Probability Lakshman Patel RJIT 292 views
1 vote
1 answer
15
For the distributions given below : Which of the following is correct for the above distributions? Standard deviation of $A$ is significantly lower than standard deviation of $B$ Standard deviation of $A$ is slightly lower than standard deviation of $B$ Standard deviation of $A$ is same as standard deviation of $B$ Standard deviation of $A$ is significantly higher than standard deviation of $B$
asked Jan 13 in Probability Satbir 523 views
1 vote
0 answers
16
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many people must be there in a ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.
asked Nov 12, 2019 in Probability Ayush Upadhyaya 262 views
1 vote
0 answers
17
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
asked Oct 23, 2019 in Probability ajaysoni1924 218 views
0 votes
1 answer
18
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n-1}$ $\frac{1}{n-2}$
asked Sep 23, 2019 in Probability Arjun 335 views
1 vote
1 answer
19
Two coins are tossed independently where $P$(head occurs when coin $i$ is tossed) $=p_i, \: i=1,2$. Given that at least one head has occurred, the probability that coins produced different outcomes is $\frac{2p_1p_2}{p_1+p_2-2p_1p_2}$ $\frac{p_1+p_2-2p_1p_2}{p_1+p_2-p_1p_2}$ $\frac{2}{3}$ none of the above
asked Sep 23, 2019 in Probability Arjun 235 views
2 votes
1 answer
20
The number of cars $(X)$ arriving at a service station per day follows a Poisson distribution with mean $4$. The service station can provide service to a maximum of $4$ cars per day. Then the expected number of cars that do not get service per day equals $4$ $0$ $\Sigma_{i=0}^{\infty} i P(X=i+4)$ $\Sigma_{i=4}^{\infty} i P(X=i-4)$
asked Sep 23, 2019 in Probability Arjun 323 views
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