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4 questions
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Joint density of two functions of a uniformly distributed random variable
I'd like to work out $\operatorname{Cov}(\cos(2U), \cos(3U))$ where $U$ is uniformly distributed on $[0, \pi]$.
I believe this involves computing $\mathbb{E}[\cos(2U)\cos(3U)]$. If so, then I first ...
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-1
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1
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Correct or Not? Probability and Geometry [closed]
A stick of length $1$ is broken into two pieces of length $Y$ and $1−Y$ respectively, where $Y$ is uniformly distributed on $[0,1]$. Let $R$ be the ratio of the length of the shorter to the ...
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1
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1
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PMF and independence with two discrete random variables?
Each of n people (whom we label 1, 2, . . . , n) are randomly and independently assigned a number from the set {1, 2, 3, . . . , 365} according to the uniform distribution. We will call this number ...
- 331
22
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3
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How to calculate the expected value of a standard normal distribution?
I would like to learn how to calculate the expected value of a continuous random variable. It appears that the expected value is $$E[X] = \int_{-\infty}^{\infty} xf(x)\mathrm{d}x$$ where $f(x)$ is the ...
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