Daneel Olivaw
  • Member for 5 years, 7 months
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3 answers
8 votes
271 views
How can I calculate $\mathrm{E}\!\left[\sum _{i=1}^X I_{\{Y_i\leq Y_{n+1}\}}\right]$?
Accepted answer
5 votes

Here is an alternative answer to @Lucas' using the law of iterated expectations: $$ \begin{align} E\left[\sum_{i=1}^X1_{(Y_i \leq Y_{n+1})}\right] & = E\left[E\left[\sum_{i=1}^X1_{(Y_i \leq Y_{n+...

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1 answers
1 votes
126 views
Stochastic ordering
Accepted answer
4 votes

According to Wikipedia: A real random variable $X$ is smaller than a random variable $Y$ in the "usual stochastic order" if: $$ \forall \ r \in \mathbb{R}, \ \mathbb{P}(X>r) \leq \mathbb{P}(...

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2 answers
2 votes
3k views
Why does SVM needs to keep support vectors?
Accepted answer
4 votes

You are right that the SVM decision function $w \cdot x + b$ depends only on $w$ and $b$, however it can be shown that $w$ can be expressed as a sum of support vectors. You can consult Stanford's or ...

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2 answers
1 votes
141 views
normalization constraint in support vector machine
1 votes

For (1), the concern is that the program $\max_{w,b}\frac{1}{\|w\|}$ is not convex: a convex program is one in which you minimize a convex function over a convex set. See @Luca Citi 's answer for more ...

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3 answers
6 votes
2k views
mean and variance of norm of normal random variables
0 votes

If $x$ and $y$ are independent, $\mu_x=\mu_y=0$ and $\sigma_x=\sigma_y=\sigma$, $r$ follows a Rayleigh distribution, thus: $$ \begin{align} & E[r] = \sigma \sqrt{\frac{\pi}{2}} \\[6pt] & V[r] ...

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1 answers
0 votes
461 views
Finding mean, standart deviation and density function of a RV
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0 votes

Let $X \sim \mathcal{N}(5,2)$ $-$ assuming 2 is the standard deviation $-$ and $Y = 2X+4$. We have: Mean: by linearity of expectation, we get: $$\mathbb{E}[Y] = \mathbb{E}[2X+4] = 2\mathbb{E}[X]+4 = ...

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