# 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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### Calculation of conditional variance for 2 correlated random variables

If we have a bivariate normal distribution for $\left(X, Y\right)$ then, we can calculate the conditional mean and variance of $\left( X|Y \right)$, as demonstrated here https://online.stat.psu.edu/...
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### Confused about Probability Density Function and Cumulative Density Function?

When computing probabilities, do we use probability density function or cumulative density function for continuous values? And I heard that if we have a cumulative density function for a set of ...
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### If a sample is normally distributed, is its population always normally distributed?

I know this is correct: "If a population is normally distributed, a sample randomly chosen from it must be normally distributed." For instance, If the sizes of all apples of my farm are ...
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### Is my data normally distributed? (QQ plot and histogram analysis) [duplicate]

I am trying to create a regression model for prediction. I need to generate prediction/confidence intervals for my model. I am trying to decide whether to use a quantile regression or linear ...
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### Equality in Gaussian Poincare Inequality

The Gaussian Poincare inequality states that: for $f: \mathbb{R}^n \to \mathbb{R}$ and $Z\sim \mathcal{N}(0,I)$, we have that \begin{align} Var(f(Z)) \le E[ \| \nabla f(Z)\|^2]. \end{align} My ...
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### What are the main difference between a QQ plot and a probability plot for measuring nomality? [duplicate]

I am trying to evaluate the normality of the distribution of my model's residuals. I have been using statsmodels.api.qqplot and ...
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### The principle of getting the error bar of the MLE of the mean of some univariate Gaussian

I'm reading the book Information Theory, Inference and Learning Algorithms. In Section 22.1, the author gives an example of finding the MLE of the mean of an univariate Gaussian, and then obtaining ...