Tagged Questions
3
votes
1answer
66 views
Expected value and variance of log(a)
I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
0
votes
0answers
25 views
Probability that a given Normal Distribution is Maximum among others [duplicate]
You are given the mean and standard deviations of N normal distributions x1,x2...xn
What is the probability that x1 is maximum?
ie. Find P(x1>x2,x3..xn)
How do I go about solving this?
x1,x2,x3 etc ...
2
votes
1answer
69 views
The sample size applied to a non-normal distribution
I have a single variable that represents my population values (sample of data):
...
2
votes
1answer
175 views
How to use Box-Muller transform to generate n-dimensional normal random variables
I'm trying to generate random variables. I read about Box-Muller transform which is a way to generate a pair of normal variables, 2-d normal distrubution. But how do I expand that transform to ...
5
votes
0answers
283 views
pdf of the product of two independent random variables, normal and chi-square
what is the pdf of the product of two independent random variables X and Y, if X and Y are independent?
X is normal distributed and Y is chi-square distributed.
Z = XY
if $X$ has normal distribution ...
3
votes
2answers
182 views
What is $P(X_1>X_2 , X_1>X_3,… , X_1>X_n)$?
All $X$ are mutually independent and from normal distributions, each with its own mean and variance. If it's easier, $P(X_1 \geq X_i \forall i \in \{1, ..., n\})$ is fine although I suspect it's the ...
2
votes
1answer
122 views
Product of Independent Gaussian Variables
Let $X$ and $Y$ be two independent normal distributions according to $X\sim\mathcal{N}(0,P)$ and $Y\sim\mathcal{N}(0,Q)$. Is it true to say the following ?
...
0
votes
0answers
74 views
Conditional Entropy of linear combination of random variables
$X_1 \sim \mathcal{N}(0,P)$, $X_2 \sim \mathcal{N}(0,P)$ and $Z \sim \mathcal{N}(0,N)$ with $X_1,X_2,Z$ mutually independent.
How do we compute
$$
H(aX_1+bX_2+Z \mid \alpha X_1+\beta X_2)
$$
where ...
0
votes
0answers
148 views
Linear combination of Gaussian random fields
I am modelling three spatial variables, $v_1, v_2$ and $v_3$ (for example, porosity, water saturation and vshale) that are correlated with each other: $\rho_{12}, \rho_{13}$ and $\rho_{23}$.
Let's ...
0
votes
0answers
214 views
Estimation of white noise parameters in Gaussian random walk model
I want to estimate the parameters (mean , variance ) $e(t)$ for the random walk model
$X (t) = X (t-1) + e(t)$.
(where $e(t)$ is the white noise with a Normal distribution).
By using the fact that ...
2
votes
1answer
512 views
Convergence of identically distributed normal random variables
I had this example in my machine learning lecture.
Let $X_2,\ldots,X_n$ be identically distributed (but not independent) copies of $X_1$ drawn from $\mathcal N(0,1)$. Then $X_n$ converges to $Y = ...
0
votes
2answers
1k views
What is the distribution of the sum of independent normal variables?
Just need to check the answer for the following question:
Question
Suppose $X$ and $Y$ are two independent standard normal variables:
$X$ ~ $N(0,1)$
$Y$ ~ $N(0,1)$
What is the distribution of $X + ...
2
votes
1answer
110 views
Few random variables cannot influence $n$ independent others too much?
I have $n$ standard normal and independent random variables $X_i$ (In reality I have a large known number of them, but let's just say I have $n$). In my experiment I want to on average get exactly 3 ...
6
votes
2answers
157 views
Inference with Gaussian Random Variable
Let $X = N(0,\frac{1}{\alpha})$, $Y = 2X + 8 + N_{y}$, and $N_{y}$ be a noise $N_{y} = N(0,1)$. Then, $P(y|x) = \frac{1}{\sqrt{2\pi}}exp\{ -\frac{1}{2}(y - 2x - 8)^{2} \}$
and $P(x) = ...
5
votes
3answers
2k views
Expectation of product of Gaussian random variables
Say we have two Gaussian random vectors $p(x_1) = N(0,\Sigma_1), p(x_2) = N(0,\Sigma_2)$, is there a well known result for the expectation of their product $E[x_1x_2^T]$ without assuming independence?
...
