I am currently writing algorithm for differential privacy using the Laplace mechanism. 

Unfortunately I have no background in statistics, therefore a lot of terms are unknown to me.
So now I'm stumbling over the term: *Laplace noise*.
 To make a dataset differential private all papers just talk about adding Laplace noise according to the Laplace distribution to the function values. 

$k(X) = f(X) + Y(X)$

(k is the differential private value, f the returned value by the evaluation function and Y the Laplace noise)

Does this mean I create random variables from the Laplace distribution according this function I have from wikipedia <https://en.wikipedia.org/wiki/Laplace_distribution>?

$ Y = μ − b\ \text{sgn}(U) \ln ⁡ ( 1 − 2 | U | ) $ 

UPDATE: I plotted up to 100 random variables drawn from the function above, but this doesn't give me a Laplace distribution (not even close). But I think it should model a Laplace distribution.

UPDATE2: 

Those are the definitions I have:

> 
> (The Laplace Mechanism).
>  Given any function $f:N^{|X|}→R^k$, the Laplace mechanism is defined as: $M\_L(x, f(·),\epsilon)=f(x)+(Y\_1,...,Y\_k)$ where Y are i.i.d. random variables drawn from $Lap(∆f/\epsilon)$ 
> 
> 
> 

As well as:

> 
> To generate
>  Y
>  (
>  X
>  ), a common choice is to use a Laplace distribution
>  with zero mean and
>  Δ
>  (
>  f
>  )
>  /ε
>  scale parameter 
> 
> 
>