All Questions
Tagged with mathematica probability
8 questions
1
vote
1
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53
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Number of simulated statistics more extreme than most extreme real data statistic
I have a distribution of $n_{obs}$ "real" data observations drawn from a normal distribution $X \sim N(\mu,\sigma^2)$, and a number $Q$ of simulated realizations of the same distribution, ...
- 13
2
votes
1
answer
205
views
Prove E[Y|X] = f(X)
I have a model $Y = f(X) + \epsilon$
where $\epsilon$ is independent of $X$ and $\mathbb{E}[\epsilon]=0, \mathbb{E}\left[\epsilon^2\right]=\sigma^2$.
Show that
$$
f(X)=\mathbb{E}[Y \mid X]
$$
This is ...
- 25
2
votes
0
answers
108
views
Maximum Uncertainty in Normal Distribution
While reading Goodfellow's Deep Learning Book, I came across the below fact about Normal Distribution. I am not sure I have understood what led to this conclusion, Can someone help with it?
"Out ...
- 51
1
vote
1
answer
34
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How to expand $\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \text{erf}\bigg(\frac{ax}{\sqrt{2}}\bigg) + \text{some_value}$?
The error function is defined as, $$\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \frac{2}{\sqrt{\pi}}\int_{0}^{\frac{(ax-b)}{\sqrt{2}}} e^{-t^{2}/2}dt$$. My question is how to expand the above ...
- 335
2
votes
1
answer
2k
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How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
- 253
2
votes
2
answers
289
views
How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
- 253
3
votes
0
answers
532
views
How do I calculate the Bayes error of a multivariate normal Bayesian classifier?
I have a 4 dimensional feature and each of them are independent normal distributions. I want to calculate the bayesian error associated with this classifier. The covariance matrix and the mean have ...
- 131
4
votes
1
answer
687
views
Chi-square independence in political sciences
I've been assigned to do a cross-class project between political science and math about the behavior of voters in a democratic state. More specifically, I'm focusing on a party from a national ...
