# Questions tagged [normal-distribution]

The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality] tag for asking about testing for normality.

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### Confidence interval for normals of normal model

Suppose $X$ is a normally distributed random variable with unknown mean $\theta$ and known variance $\sigma_{X}^{2}$. Suppose that $Y_{1}, \ldots, Y_{n}$ are random variables that, conditioned on $X$, ...
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### How general is this property about correlation and the sum of two normal RVs?

(Cross-posted from math stack exchange as I didn't get any responses there) Given a random vector $(X_1,X_2)$ that is jointly normal with means / sd's $\mu_1,\mu_2, \sigma_1,\sigma_2$ and correlation ...
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### Statistical analysis of carbon dioxide flux data

I have been measuring flux of CO2 in (mmol m-2 d-1) from two different rivers and I now want to do a statistical analysis using IBM SPSS but I'm not sure where to start. One lake is showing negative ...
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### Asset prices are in theory log-normally distributed

In finance, the price of an asset is given by the following formula. $P_t=P_0* e^r$ r=returns Pt = Price at time "t". P0 = Actual Price. Likewise, it is assumed that the yields (r) will ...
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### Simplifying the Kullback-Leibler divergence for a sum of distributions

I want to find an approximation of a mixture of probability distributions that minimises the Kullback-Leibler divergence (KLD). I need to verify my result, as it seems suspect. We have a joint ...
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### Density of Multivariate Normal Distribution (MVN): Dimension = 1 or k?

I have a very naive question about the density function of the MVN distribution. According to the wiki page, the density function formula sometimes has a constant k ...
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### How is the difference between 2 normal distributions a normal distribution? [duplicate]

I've learned that if we sum or subtract 2 normal distributions, the result would be another normal distribution with $\mu=\mu_{1}\pm\mu_{2}$ and $\sigma=\sqrt{\sigma_{1}^2+\sigma_{2}^2}$ https://www....
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### Variational Inference Mean-Field Gaussian

I am new to variational inference and got very confused about some basic ideas. We want to use the mean-field gaussian family to approximate a complicated high-dimensional distribution. I want to ...
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### Distribution of Residuals and Response - When to use which?

I would like to analysze the relation between my continuous response 'soil moisture content [%]' and 2 categorical and 1 continuous predictors. I fit a linear mixed model and checked the distribution ...
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