Tagged Questions

Questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution.

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Multivariate Normal Distribution: Relationship between two conditional probabilities.

Suppose I have a multivariate normal random variable $Z$ which has $n$ dimensions. Suppose I have a vector $x$. Set $i$ as a number between $1$ and $n$ and $k$ as a number between $1$ and $n-1$. Can ...
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If $0< 2\varepsilon < \sigma^2 < 1$ then $\prod\limits_{i = 1}^n (1 + \varepsilon + \sigma \xi _i )$ converges almost surely to $0$

I posted this question a few days ago and there were some errors in my post. I have fixed them and it should be all right now. Hope someone can help with my confusion. Let $(X_n)_{n\ge0}$ denote an ...
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Find all solutions of $f$ such that $\operatorname{Cov}(f(x),x)=c$ where $x \sim N(\mu,\sigma^2)$ and $c$ does not depend on $(\mu,\sigma^2)$

Find all solutions of $f$ such that $$\operatorname{Cov}(f(x),x)=c$$ where $x \sim N(\mu,\sigma^2)$ and $c$ does not depend on $(\mu,\sigma^2)$ I think the only solution is $f$ is constant (almost ...
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What do we know about the sum of two dependent lognormal random variables (without assuming underlying joint normality)?

Let $V\sim\mathcal N(0,\sigma^2)$ and $W\sim\mathcal N(0,\zeta^2)$ marginally, but without any assumption of being jointly normal. For given constants $a$ and $b$ (real, or maybe restricted to ...
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distributions with kurtosis

I have a stream of events from a large set, S. I am counting their residues modulo c in a set of counters. (c is much smaller than the cardinality of S.) If all of the S events were equally probable,...
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Create Normal Distribution Curve for Data

Following this tutorial I would like to plot normal distribution curve for following data ...
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Evaluation of the integral of a linear gaussian model?

suppose the following $$P(x_1) \text{ ~ } N(7.3555\ ; 12.3433)$$ and $$P(x_2|x_1) \text{ ~ } N(0.995\ + \ 0.2351x_1\ ;13.732)$$ how to evaluate the following integral? \begin{align*} \int \mathcal{I}...
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Covariance estimation and Graphical Modelling

I've started reading on Convariance Matrix estimation through Graphical model in high-dimensional situation. But I have several questions. Suppose, $X_i \overset{iid}{\sim} N_p(\mu,\Sigma)$, $i=1(1)n$...
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Sum of two normal distributions

Question: N(µ,σ) ξ ε N(3,4) ; η ε N(1,3) What is 3ξ + η? I'm new to normal distributions, and not even sure if this is called "sum of normal distributions". I ...
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Find the probability of getting 20 heads in 40 flips of a fair coin

Find the probability of getting $20$ heads in $40$ flips of a fair coin I did this problem with the binomial distribution and got my probability as $0.12537$. However, I am being asked to do this ...
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Can we take two temperature ranges for this probability?

"Electronic sensors of a certain type fail when they become too hot. The temperature at which a randomly chosen sensor fails is T ºC, where T is modelled as a normal random variable with a mean of ...
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