Linked Questions

1
vote
0answers
36 views

Gaussian random variables [duplicate]

Can some one help me point in the right direction or point to some resources that will help me prove that sum of two jointly distributed Gaussian r.v. with a given correlation coefficient is also a ...
13
votes
2answers
20k views

Linear combination of two dependent multivariate normal random variables

Suppose we have two vectors of random variables, both are normal, i.e., $X \sim N(\mu_X, \Sigma_X)$ and $Y \sim N(\mu_Y, \Sigma_Y)$. We are interested in the distribution of their linear combination $...
7
votes
1answer
7k views

The product of two lognormal random variables

Let $X_1$ and $X_2$ be two normal random variables. Write $X_1\sim N(\mu_1, \sigma^2_1)$ and $X_2\sim N(\mu_2, \sigma^2_2)$, to fix ideas. Consider the corresponding log-normal random variables: $...
4
votes
1answer
7k views

How to compute a probability threshold for a linear combination of two variables ~ N(0,1)?

I have a variable which is a linear combination of two other variables, each one following an N(0,1) distribution. I need to compute the threshold of the distribution of this combination variable (to ...
0
votes
3answers
5k views

Standard deviation of the sum of two normally distributed random variables

$X\sim N(52,6)$, $Y\sim (40,8)$. What's the standard deviation of $Z=X+Y$? I'm considering to transform the linear relationship to matrix form $$Z=\begin{pmatrix} 1& 1\\ \end{pmatrix}\begin{...
3
votes
1answer
1k views

Sum of Gaussian is Gaussian?

As a newbie in probability, I am recently cleaning my understandings about Gaussian distribution. I know that If $X$ and $Y$ are jointly Gaussian, then $aX+bY$ ($a$ and $b$ are both constant) is ...
4
votes
1answer
1k views

Joint distribution of sum of independent normals

Suppose we have three independent normally distributed random variables $$ X_0 \sim \mathcal{N}(\mu_0, \sigma_0^2), $$ $$ X_1 \sim \mathcal{N}(\mu_1, \sigma_1^2), $$ $$ X_2 \sim \mathcal{N}(\mu_2, \...
7
votes
1answer
238 views

Generate identically distributed dependent normal random numbers with prespecified sum

How do I generate $n$ identically distributed but not independent normal random numbers such that their sum falls within a prespecified interval $[a,b]$ with probability $p$? (This question is ...
1
vote
2answers
101 views

Is the joint distribution of two linear combinations of Gaussians still a multivariate normal?

Suppose I have $\textbf{X}$ ~ $N(\textbf{0},\Sigma)$, and I'm considering two different linear combinations, $a^* X$ and $b^* X$, which we suppose are uncorrelated. I understand that linear ...
1
vote
1answer
136 views

Flying Bomber aircraft through SAM sites - combining normal distributions

I have been puzzling over this for days but I don't think this was covered at school We simultaneously fly a known number of bomber aircraft, K, through three sequential batteries of surface to air ...
0
votes
0answers
24 views

How to show via Delta method that the Linear Taylor series expansion of a normal random vector results in NORMAL DISTRIBUTION [duplicate]

How can it be proved using the delta method that the Linear Taylor series expansion of a normal random vector containing independent but NOT identically distributed elements results in a random ...