# Questions tagged [random-variable]

For questions related to the mathematical concept of a random variable (in the context of AI).

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### Is learning possible without random thoughts and actions?

In my view intelligence begins once the thoughts/actions are logical rather than purely randomn based. The learning environments can be random but the logic seems to obey some elusive rules. There is ...
104 views

### What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?

I know that the notation $\mathcal{N}(\mu, \sigma)$ stands for a normal distribution. But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation:...
54 views

### What kind of distributions can be used to model discrete latent variables?

If we take the vanilla variational auto-encoder (VAE), we $p(z)$ is a Gaussian distribution with zero mean and unit variance and we approximate $p(z|x) \approx q(z|x)$ to be a Gaussian distribution as ...
53 views

### In the definition of the state-action value function, what is the random variable we take the expectation of?

I know that $$\mathbb{E}[g(X) \mid A] = \sum\limits_{x} g(x) p_{X \mid A}(x)$$ for any random variable $X$. Now, consider the following expression. \mathbb{E}_{\pi} \left[ \sum \limits_{k=0}^{\infty}...
23 views

### What machine learning model should I use for a random dice-based game?

Consider a game like Pig (https://en.wikipedia.org/wiki/Pig_(dice_game)), but with a few additions: namely functions of both player's score and turn number that have unique impacts on scoring. What ...
35 views

### Why is this variable in equation 2 of the SQAIR paper a random vector of $n$ ones followed by a zero?

I've been reading the SQAIR paper lately, and the mathematics involved seems a bit complicated. Some background, about the paper: SQAIR stands for Sequential Attend, Infer, Repeat - the paper does ...