Questions tagged [variance]

For questions regarding the variance of a random variable in probability, as well as the variance of a list or data in statistics.

1,173 questions
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Determining variance from sum of two random correlated variables

I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated?
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A simple variance question

Say I am paid 1 million dollars per pip on a six sided dice and I roll the dice one time. Now compare this to a game in which I get 1 dollar per pip on a dice, but I roll the die one million times. It ...
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Proof of Variance of the Irreducible Error

In Introduction to Statistical Learning, given the general form of a quantitative response between a set of predictor variables and a target variable $$Y=f(X)+\epsilon$$ and the general form for a ...
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A measure similar to variance that's always between 0 and 1?

Consider the following histogram, obtained from around 1000 measures of distance. As you can observe, most of the data appears near the mean arond the value 5-10. I also have some isolated samples ...
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Taking the average after randomly knocking out members

I'm looking at a random variable that takes vectors $\newcommand{\vv}{\mathbf{v}} \vv_1, \dotsc, \vv_n \in \mathbb{R}^d$ and calculates their average, after applying "blankout" noise to them. So we ...
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Terms in a stochastic differential equation

In the mathematics of finance, a stochastic process can be given by a stochastic differential equation: $$dX_t = a(X_t,t)dt + b(X_t,t)dB_t$$ where $dB_t$ is a Wiener process. What is the basic reason ...
Let $X,Y$ be independent RVs. If there exists $c \in \mathbb R$ s.t. $P(X+Y=c)=1$, then $X,Y$ are constants
I would like to show: Let $X,Y$ be independent RVs. If there exists $c \in \mathbb R$ s.t. $P(X+Y=c)=1$, then $X,Y$ are constants a.s.. What I tried: Since X,Y are indep,1=P(X+Y=c)=\int 1_{...
Let $\left(\mathcal{D}_{n}\right)_{n\in\mathbb{N}}$ be a family of probability distributions such as: $\forall n\in\mathbb{N}$, $\mathbb{E}\left[\mathcal{D}_{n}\right]=n$: the average value of the n-...