# Questions tagged [variance]

The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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### Convergence of variance of sample median

In this SE question, it is stated that there is a central limit theorem for the sample median, namely $$\sqrt{n}(Y_n - m) \xrightarrow{d} N(0, [2f(m)]^{-2}),$$ as $n\to\infty$ where $Y_n$ is the ...
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### Variance of projected data

What's the expression for the variance of projection of $N$ data points onto a vector $\mathbf{v}$ which is not necessarily a unit vector? I could only find an expression when $\mathbf{v}$ is taken to ...
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### Second order with Delta method on a ratio to improve variance estimation accuracy

Following a previous post on math exchange without success, I have applied the "Delta method" that says : Delta method : There are alternative formulations of this expression which may be ...
1answer
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### Portfolio theory: confusion about variance-covariance matrix

I am taking an introductory course to finance in my Master's, and wanted to go further in the topic of portfolio theory (I am an engineering bachelor graduate, but as I just hinted, I am new to ...
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### Variance of predicted value in a linear regression when $n \to \infty$

The following question is from Kutner's Applied Linear Statistical Models - Ch 2 - 2.12 To answer the question a few pieces of information are needed, provided below: What I gather the question is ...
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### Explaining and Addressing the Bias-Variance Tradeoff

Let's say we have a model whose training error is 7% and the validation error is 10%. What does this mean in terms of the bias-variance tradeoff? I know that high validation error and low training ...
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### Interpreting divergence between standard error and observed standard deviation of population

I have a simple dataframe. Users come to my website and sign up for a trial. I consider each sign up as a conversion. But my conversion rate is fluctuating wildly every day even though I have about ...
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### Associate uncertainities to variance's estimate of a distribution with heavy tails

I have a set of $M$ variables $\{ \lambda_N^{(i)} \}_{i=0}^{M(N)}$. The distribution of $\lambda$ depends on the $N$ parameter; for $N \rightarrow \infty$ the distribution shrinks around the mean ...
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### Object cloning expected value and variance

Suppose there exist special marbles that can clone themselves while keeping their special cloning ability. The probability that any special marble independently clones itself is 0.01/sec (i.e. there ...
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### Estimate how many values fall below a specific deviation using the empirical rule

I'm trying to estimate how many values fall within a portion of the standard deviation Lets say I have: A sample size of 100 and Average of 50. and a start deviation of 10. Using the Empirical Rule ...
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### Looking for a measure of variance of variance?

I was hoping you would be able to help me identify the statistic I am looking for, or point me in the right direction. Is there a statistical measure that will represent variance of variance (or s.d. ...
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### Can we derive the Variance of the least squares slope WITHOUT assuming that $X_i$s are fixed or deterministic? [duplicate]

Everywhere in the literature, I have seen that while deriving the variance of the least squares slope estimate $Var(\hat \beta_1) = \dfrac{\sigma ^2}{SS_{xx}}$, we always assume that $X_i$s are fixed ...