# Tagged Questions

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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### Fourier transform of white noise - Phase and magnitude?

Assume that $X(t)$ describes white noise in time, with $\langle X(t) \rangle =0$ and $\langle X(t) X(t') \rangle = \sigma^2 \delta(x-x')$. I want to know the distribution of it's Fourier transform. ...
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### Variance Reduction by Conditioning

Say that given Y=y, (edit->) a R.V. (edit end) N have a probability function of $f_N$ and Y have a distribution function $F_Y\in(0,1)$. We want to estimate the the probability p for when N is larger ...
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### If $\text{Var}(X) < \infty$, is $\text{Var}(XY) < \infty$ for $0 \le Y \le 1$?

I have a variable $X$ that I know has finite variance (and therefore also finite mean). Is it always true that its variance remains finite after scaling by $0 \le Y \le 1$? Note that $X$ and $Y$ are ...
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### How to calculate variance contribution in a Zero-Inflated Poisson regression?

I was wondering if anyone has an idea on how to calculate the contribution to variance of each independent variable in a Zero-Inflated Poisson. How would it even work if you actually have two models ...
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### Test for equal variance for 2-way ANOVA

Forgive a novice in statistics for asking a perhaps very simple question, but I am running a two-way ANOVA with unbalanced design and want to test for homoscedasticity using Levene. For a one-way ...
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### Variance explained $R^2$ by separate fixed effects (and interactions)

I am currently assessing the effect of five environmental variables (A, B, C...) on a trait (Y). I would like to estimate how much variance in Y each environmental variable explains. Previously I had ...
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### What is zero mean and unit variance in terms of image data?

I am new to deep learning. I am trying to understand some concepts. I know "mean" is an average value and "variance" is deviation from mean.I have read some research papers, all say that we ...
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### What's up with this variance computation?

I'm trying to re-implement the Ckmeans.1D.DP algorithm in Python. I have the actual dynamic optimization part down, but I'm a little confused by the BIC computation they use for selecting the number ...
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### Negative variance result when calculating standard deviation

Please note, I am still in secondary school so please keep your answers simple. A question on my homework states to calculate the standard deviation from a given frequency table with several class ...
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### If X~Exp(λ), what is the expected value of Y=X²?

I am trying to compute this using the integral definition of expected value but I don't think I am doing it right as I am getting a very hard integral that I can not solve. When computing ...
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### Difference between volatitlity of Annualized return and Annualized volatility of returns

I have a series of monthly returns on financial data. My goal is to estimate the volatility of 10 year rolling returns. I am a bit confused on two options. a) Calculate 10 year rolling returns, ...
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### Volatility of investment (/w currency hedging)

I´ve been trying to compute volatility of investment with currency hedging, and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% ...
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### What is the difference between R2 and variance score in Scikit-learn?

I was reading about regression metrics in the python scikit-learn manual and even though each one of them has its own formula, I cannot tell intuitively what is the difference between R2 and variance ...
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### Statistical analysis for replication in very small experimental datasets

A colleague does replication on a quite coslty experiments. There are four different conditions, each one duplicated. The outcome with $4\times 2 = 8$ points is illustrated below: The analysis is ...
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### There are many statistical erros in this results and discussion. Can someone help me locate them? [closed]

Results: Data Coding and Exploratory Data Analysis All data were entered into a single SPSS data file for analysis. Seven variables were coded: 1. Sex 2. Total amount of television viewing hours ...
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### How many boxes have balls?

I have N boxes, each of which may or may not contain a ball. I want to know how many boxes have balls by sampling the boxes in the following way. For each box in the N boxes: I open this box with ...
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### Variance estimation for Levy process

Let $(X_t)$ be a Levy process. It then holds that $$E(X_{t+\Delta} - X_t) = \Delta \nu, \\ V(X_{t+\Delta} - X_t) = \Delta \mu,$$ under sufficient regularity conditions in terms of moments. For ...
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### Assessing overall variation for each case in panel data

I have a panel data set - a score on a single measure for hundreds of people, taken once per day for all 365 days of a year. I'm looking for the best method to assess overall variation within each ...
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### How to change your data to be homoscedastic?

I want to use a linear discriminant analysis and need homoscedasticity. I'm wondering how to get this assumption correct with the data that I have. I have in total over 7000 samples, but I'm ...
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### Choosing Predictor values to minimize Variance of Least Squares Estimator

Suppose the values of $-1≤ x(i) ≤ 1$ are at your disposal in the simple linear regression model $Y(i) = α + βx(i) + ε(i)$, where the $ε(i)$ are i.i.d. $N(0, σ^2)$. How would you choose the $x(i)$ if ...
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### How do the means of $X^2$ and $X$ compare?

If $X$ has an exponential distribution with mean $\theta$, does $X^2$ have mean $\theta^2$? If not, how would I find the variance of $X^2$? I tried this: $$V(X^2) = E[X^4] - E[X^2]^2$$ But I'm ...
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### Data violates homogeneity of variances and is not normally distributed. Can I still run the t-test?

I have two categorical, independent groups, and a continuous dependent variable. The data violates homogeneity of variances, and the dependent variable is not normally distributed for each of the two ...
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### Does rounding introduce variance into estimates?

It is often recommended to round parameter estimates to avoid suggesting more precision than the data really have, e.g. here. I understand rounding does not introduce bias, as long as an unbiased ...
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### Compute confidence interval for univariate Kernel Density Estimator

I've got a univariate dataset (timeseries) for two kind of simulated systems, and I want to explore the differences between the two. To do that, I can build a univariate gaussian KDE for each dataset ...