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16 views

Generate Correlated Normal and Log-Normal Random Variable

The standard approach for generating two normally distributed random variables some with correlation $\rho$ is explained here: Generate Correlated Normal Random Variables. Now let $X,Y$ be normally ...
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0answers
7 views

covariance and correlation of two three dimentional gaussian distributions

Lets say we have 'n' three dimensional dimensional gaussian distributions with a '3' dimensional mean vector and 3 x 3 non-diagonal covariance matrix. How can I check if they are correlated? Is ...
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1answer
20 views

Does correlation have to be in the context of (Gaussian) normal distribution?

I am not quite familiar with the concept of correlation. The Pearson's correlation coefficient is defined as: $\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ...
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1answer
207 views

Distribution of the sum of normal random variables

Let $X\sim \mathcal N(\mu_X,\sigma_X^2),\ Y\sim \mathcal N(\mu_Y,\sigma_Y^2)$ two normal random variables and $a,b\in \mathbb R$. If $X,Y$ are independent, then $$aX+bY\sim \mathcal ...
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1answer
62 views

How can we derive expectation of two dependent normal distribution?

$\mathbf{X}$ and $\mathbf{Y}$ are each dependent normal random variable, then how can we derive like this one? $$\mathbf{E}\{e^{\mathbf{X}}e^{\mathbf{Y}}\}$$ I know the each first moment is ...
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1answer
45 views

Generating correlated random numbers from Normal Distributions

If I have a sequence taken from X~N (μ1 , σ1 ). Is it possible to generate a sequence of numbers drawn from Y~N (μ2 , σ2) such that X and Y have correlation ρ?
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1answer
70 views

Countermonotonicity and minimum linear correlation coefficient

In an example exercise they question whether it is possible to construct a bivariate distribution of $LN(0,1)$- and $LN(0,4)$-distributed random variables, where $LN(\mu,\sigma^2)$ is the log normal ...
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0answers
34 views

Correlation: How to extend it from pairs to further random variables?

How can one determine the correlation coefficients (or their intervals) between $n$ standard-normal random variables $X_i$, $i=1,...,n$, when $X_i$ correlates with $X_{i+1}$ with correlation ...
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1answer
66 views

Interval of non-uniformly distributed set of numbers adjusted that it properly excludes extremes

Let's say I have an interval of numbers from 1 to 9 with the following frequency of distribution: numbers 1, 2 and 3 about 20 occurrences number 6 has 2 occurrences and number 9 has only ...
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0answers
71 views

Finding Correlation between two types of Normally distributed data.

I have predictions and real outcomes for 6 projects of 2 different types (let's say type1 and type2). Is it possible to calculate the correlation between the two types? Predictions of the outcome: 3 ...
1
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1answer
106 views

Correlation of sums of correlated variables

I'm trying to work out an expression for a correlation of the weighted sums of two r.v.'s with a third r.v. To be precise, I have a trivariate normal distribution: $$\{X,Y,Z\}\approx ...
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1answer
153 views

special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
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1answer
95 views

Does $0$ correlation imply independence for marginally normal distributions?

Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$. Can someone give a hint why this is true ?
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1answer
676 views

Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent)

Would like to know how to approach this question: Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent). Seen the solution for the ...
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1answer
301 views

Calculate Correlation between 2 values

I have a random vector $X = ( X_1 , X_2 )$ that has a bidimensional normal repartition with mean $0$ and covariation matrix : $$ \Sigma = \left( \begin{array}{ccc} 1 & q \\ q & 1 ...