# Questions tagged [random-variable]

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

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### 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}...
79 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:...
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 ...
49 views

### Should the biases be zero or randomly initialised?

I'm initialising DNN of shape [2 inputs, 2 hiddens, 1 output] with these weights and biases: ...
40 views

### What is the point of converting conditional probability to factor for Variable Elimination?

I have this slide from my AI class on using a Bayes network to compute a conditional probability. I don't really understand the point of converting the conditional probabilities to factors (besides ...
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 ...