Question

Probability for all pairs $(x,y)$ with $x,y\in{[0,1]}$ that $\theta= \cos^{-1}\frac{-y^2+y-x^2}{\sqrt{x^2+(y-1)^2}\sqrt{x^2+y^2}} < 90^\circ$

score 40 · Answer 1 · 2026-03-28 06:59:45

40

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Probability for all pairs $(x,y)$ with $x,y\in{[0,1]}$ that $\theta= \cos^{-1}\frac{-y^2+y-x^2}{\sqrt{x^2+(y-1)^2}\sqrt{x^2+y^2}} < 90^\circ$

Published on 28 Mar 2026 - 6:59

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1.8k

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2.5k

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211

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score 204 · Answer 6 · 2026-04-01 10:44:37

204

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112

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List Question

Probability for all pairs $(x,y)$ with $x,y\in{[0,1]}$ that $\theta= \cos^{-1}\frac{-y^2+y-x^2}{\sqrt{x^2+(y-1)^2}\sqrt{x^2+y^2}} < 90^\circ$

Knowing that $\phi$ is a characteristic function, show that $e^{\phi-1}$ is also a characteristic function

Find the pdf of a new random variable that is a power of a uniform distribution

Fair Coin Winnings

roll a die an infinity of times and probability that the maximum among all the numbers obtained is 5

Help to prove $\sum_{i=1}^n(X_i-\overline{X})(\overline{X}-\mu)=0$.

HMM with hidden outcomes, knapsack problem

Sampling Distribution of Difference of Normal Random Variables

Sampling Distribution and Chi Squared Random Variables

Probability After Sampling Without Replacement Until Success

Conditional expectation: treating $X_1$ as constant?

Variance of $S^2$ taken from Normal Distribution

Information transmitting rate of a noisy discrete channel with Omission/Adding errors

Computing Conditional Probability on Birthday Problem

Correlation of all zero rows and columns in matrix

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