# Tagged Questions

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

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### Normal distribution and choosing final number

I've read a paper which used normal distribution in order to assign a number to each entity as follows: Each user has a quality measurement qi ∈ [0, 1]. For the experiments in this paper, the ...
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### How to calculate inverse cumulative distribution using a table?

I need help with this: $$P(X\geq a)=1-F_X(a)=1-\Phi\left(\frac{a-70}{8}\right)=0.25$$ When $X\sim N(70,64)$. I know that it should be: $(a-70)/8 = 0.6745$ How do I get $0.6745$ From $Z$ table? I ...
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### Significance and Poisson processes

Must I include the Poisson error on a new observation when considering whether it is consistent with a distribution? For example, the number of rain drops that fall into a cup per minute are recorded....
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### Generalized law of large numbers

Do you know any kind of generalisation of the law of large numbers. I mean something like this : Assume that $(X_n)_{n\in\mathbb{N}}$ is a sequence of independant variables (not necessarily ...
31 views

### Show how Gaussian with mean $\mu$ and std dev $\sigma$ is constructed.

I am a computer science student, who has recently taken an interest in data science. I've been learning about Gaussian distributions, and I've read from the documentation of the numpy python package ...
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### Why does the normal distribution describe data collected in real life so well? [on hold]

$$P(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp \left( - \frac{(x-\mu)^2}{2\sigma^2} \right)$$ Is there any intuition behind choosing $e^{-x^2}$ instead of some other function?
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### $\lim X_n = 0$ iff $b > 0$

Probability with Martingales: It looks like $$\lim \exp\{aS_n - bn\} = 0$$ if $b > 0$ because $$\lim aS_n - bn = -\infty \tag{*}$$ but how to prove $(*)$?
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### Conditional expectation of independent normals

As it was proved in the answer here, for $Z_1, Z_2$, two independent and identically distributed random variables. Then we have: $$\mathbb E[Z_1\mid Z_1+Z_2] =\frac{Z_1+Z_2}{2}.$$ However, suppose ...
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### Existance of a UMVUE [on hold]

$\{X_{i}: 1\leq i \leq n \}$ is a random sample, i.i.d $N(\mu, 1)$ with $\mu$ unknown. For a fixed $x_{0}$, does there exist a UMVUE for $\phi(x_{0}-\mu)$, where $\phi$ denotes standard ...
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### Normal distribution

can anyone help me calculate $E(Z^4)$, $E(Z^3)$ for $Z\sim N(0,1)$? I know that $Z^2\sim \chi^2(1)$ then $E(Z^2)=1$, $Var(Z^2)=2$. Thank you.
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### I am trying to find answer to this bivariate normal problem. Can anyone help. [closed]

The distribution of the heights of husband-wife pairs in a particular population is modelled by a bivariate normal distribution. The mean height of the women is 165cm and the mean height of the men is ...
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### If $(W_t)_{t\ge 0}$ is a $L^2(D)$-valued Wiener process, then $W_t(x)$ is normally distributed

Let $d\in\mathbb N$ $\lambda$ denote the Lebesgue measure on $\mathbb R^d$ $D\subseteq\mathbb R^d$ be a domain $U:=L^2(D)$ and $\langle\;\cdot\;,\;\cdot\;\rangle:=\langle\;\cdot\;,\;\cdot\;\rangle_U$...