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Title: Covariance and Correlation
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Series: Probability Theory
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YouTube-Title: Probability Theory 19 | Covariance and Correlation
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Bright video: https://youtu.be/0XvJ6NOemEU
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Dark video: https://youtu.be/zbEFOPUbsTs
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: pt19_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space and $X \colon \Omega \rightarrow \mathbb{R}$ be a random variable. What is the covariance $\mathrm{Cov}(X, X^2)$?
A1: $\mathbf{E}(X^3) - \mathbf{E}(X^2)\mathbf{E}(X)$
A2: $\mathbf{E}(X^2) - \mathbf{E}(X)\mathbf{E}(X^4)$
A3: $\mathbf{E}(X^2) - \mathbf{E}(X)\mathbf{E}(X^2)$
A4: $\mathrm{Var}(X) - \mathbf{E}(X)^2$
Q2: Let $X, Y$ be two random variables with $\mathrm{Cov}(X,Y) = 1$. Can they be independent?
A1: No, never!
A2: Yes, always!
A3: There are examples such that they are independent but in general they are not.
Q3: Let $X,Y$ be normally distributed with $\mathrm{Cov}(X,Y) = 0$. What is correct?
A1: $X,Y$ are independent.
A2: $X,Y$ are not independent.
A3: The correlation coefficient is 1.
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Last update: 2024-10
