# Tagged Questions

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

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### Normal distribution with sample

I'm trying to figure out the best approach to this problem. I would assume that I can use the Central Limit theorem first and then a binomial cdf: Chocolate is packaged into jars using a computerized ...
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### Multivariate normal density function of function of random variable

Let $X_1,\dots,X_n$ be i.i.d random variables and $g$ be a symmetric function such that $$g(X_i,X_j)\sim N(\mu,\sigma^2)$$ for all $1\le i<j\le n$. I wish to know the density function of the joint ...
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### If X + Y is truncated normal and X and Y are identitically (but not independently) distributed? What is the distribution of X and Y?

Let $(aX + bY)$ be a truncated normal and assume $X,Y$ are both identically distributed (but necessarily NOT independent) what is the distribution of $X$ and $Y$? More importantly can the pdf of $X$ ...
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### Normal Distribution Approximations and Central Limit Theorem

Let $X_1,\ldots,X_{144}$ be a random sample from a population with mean $\mu = 20$ and variance $\sigma^2 = 64$. (a) What is the approximate distribution of $\bar X$? (b) Find $P( \bar{X} < 19)$....
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### Calculate multivariate Gaussian from univariate Gaussian

I am currently trying to solve an exercise that involves estimating the position $\chi_t$ and and velocity $\dot\chi_t$ of a truck at time $t$. The truck moves on rails and is buffeted around by a ...