Xavier Initialization - Formula Clarification

Problem : How is a $W_i$ calculated when using Xavier initialization?

From what I understand, the Xavier initialization calculate de sttdev, but Im not sure how it uses that for calculating a specific weight value.

According to the references, $W$ is the "initialization distribution for the neuron in question", what does that mean ? How does that even decide what the value will be?

For a current Layer, let $s$ be the output connections of the layer and $e$ the input connections, then: $f(W) = \frac{2}{e + s}$

References:

http://philipperemy.github.io/xavier-initialization/

http://andyljones.tumblr.com/post/110998971763/an-explanation-of-xavier-initialization

https://prateekvjoshi.com/2016/03/29/understanding-xavier-initialization-in-deep-neural-networks/

https://www.quora.com/What-is-an-intuitive-explanation-of-the-Xavier-Initialization-for-Deep-Neural-Networks

CNN xavier weight initialization

In the case of Xavier initialization (also called "Glorot normal" in some software), the parameters are initialized as random draws from a truncated normal distribution with mean 0 and standard deviation $$\sigma = \sqrt{\frac{2}{a+b}}$$ where $a$ is the number of input units in the weight tensor, and $b$ is the number of output units in the weight tensor.