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High School
By
True IITJEE
on May 29, 2014 | Updated Jan. 3, 2018
JEE-Main 2013 Mathematics 35
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even aft…
Mathematics
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jee main
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Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Runs in coin tosses
You have a biased coin i.e., each coin toss is a head with probability \(p\) and is a tail with probability \(1-p\). Let \(X\) be the number of runs in \(n\) independent tosses of this coin. Here, run…
Mathematics
Probability
expectation
variance
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Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Triangles in a random graph
Let \(G = G(n, \frac{1}{2})\) be a random graph on \(n\) vertices, i.e., for each pair of verices \(i, j\), we add the edge \((i, j)\) independently with probability \(\frac{1}{2}\). Let \(T_n\) be th…
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variance
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Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Basics of Expectation and Variance
If the random variable \(X\) takes values in non-negative integers, prove that: \(E[X] = \sum_{t=0}^\infty \Pr(X > t)\) Prove that if \(X_1\) and \(X_2\) are independent random variables then …
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