Linked Questions
89 questions linked to/from What is the intuition behind conditional Gaussian distributions?
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Bivariate normal distribution , link $\Bbb E(Y\mid X=x)$ and $\Bbb E(X\mid Y=y)$ [duplicate]
Note: I edited this question on 1/1/2018 because of the comments on the original question. So some comments relate to the earlier version. It is closed as duplicaten but I dusagree with that
For a ...
user83346
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Epsilon from Bivariate Normal Distribution [duplicate]
I came across the following example from a book. I am given a dataset generated from a bivariate normal distribution:
Among the data, there are missing values for the last 20 of x2i (but not for x1i)....
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Let X,Y be bivariate normal , what is E[X|Z] where Z = X + Y? [duplicate]
I am trying to understand how does expectation and variance looks when
Let X,Y be bivariate normal
I want understand E[X|Z] and Var[X|Z]
when Z = X + Y
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Proof for bivariate conditional mean of Gaussian dist [duplicate]
I see that a lot of questions are answered here for multivariate and bivariate conditional distributions. But I did not find the proof of these equations (I need just for bivariate case).
to get this
...
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properties of conditional normal random vectors [duplicate]
Given the partitioning: $X =
\begin{pmatrix}{}
x_1 \\
\
x_2
\end{pmatrix}$ for a normal random vector with mean $\mu =
\begin{pmatrix}{}
\mu_1 \\
\
\mu_2
\end{pmatrix}$ and covariance matrix:
$\...
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Prove that the conditional distribution of a normal random variable is also normal random [duplicate]
How to prove the claim that the conditional distribution of a normal random variable is also normal random? And how to think it intuitively?
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Assessing approximate distribution of data based on a histogram
Suppose I want to see whether my data is exponential based on a histogram (i.e. skewed to the right).
Depending on how I group or bin the data, I can get wildly different histograms.
One set of ...
- 1,201
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Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?
The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other ...
- 1,575
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How does the formula for generating correlated random variables work?
If we have 2 normal, uncorrelated random variables $X_1, X_2$ then we can create 2 correlated random variables with the formula
$Y=\rho X_1+ \sqrt{1-\rho^2} X_2$
and then $Y$ will have a correlation ...
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Understanding the confidence band from a polynomial regression
I'm trying to understand the result I see in my graph below. Usually, I tend to use Excel and get a linear-regression line but in the case below I'm using R and I get a polynomial regression with the ...
- 569
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What is the intuition behind the independence of $X_2-X_1$ and $X_1+X_2$, $X_i \sim N(0,1)$?
I was hoping someone could propose an argument explaining why the random variables $Y_1=X_2-X_1$ and $Y_2=X_1+X_2$, $X_i$ having the standard normal distribution, are statistically independent. The ...
- 21.1k
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Generate normally distributed random numbers with non positive-definite covariance matrix
I estimated the sample covariance matrix $C$ of a sample and get a symmetric matrix. With $C$, I would like to create $n$-variate normal distributed r.n. but therefore I need the Cholesky ...
- 461
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Why does Covariance measure only Linear dependence?
1) What is meant by linear dependence?
2) How can I convince myself that covariance measures linear dependence?
3) How I can convince myself that non-linear dependence is not measured by covariance?...
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Sign of product of standard normal random variables
The question is mainly in the title:
Given two standard normal random variables with correlation $\rho$, what is the distribution of sign of their product?
I understand that when $\rho=0$, we have ...
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What do vertical bars mean in statistical distributions?
What do the vertical bars mean in the first and third formulae?
$$v_i|z_i=k,\mu_k\sim\mathcal{N}(\mu_k, \sigma^2)$$
$$P(z_i=k)=\pi_k$$
$$\pi|\alpha\sim \text{Dir}(\alpha/K1_K)$$
$$\mu_k\sim H(\lambda)...
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