# Plotting a Probability distribution with varying parameter

Suppose I wish to plot the function

```
import numpy as np
var('a,y')
A=np.linspace(-1,1,10)
for a in A:
z=a+x-(e^(-y^2/2))/sqrt((2*pi))
plot3d(z,(x,-1,1),(y,-1,1))
```

That is, I wish to plot the function `z`

over a range of `a`

. Actually the original function was `z=a+x`

. But, in order to introduce randomization, I changed the variable `x`

to `x-y'`

, where `y'`

is the standard normal variable. I wish to obtain the plot of `z`

as a kind of variable probability distribution over the grid of `x`

and `y`

with the variation of `a`

(so kind of series of probability distributions overlapping each other). How do I do this? Any hints? Thanks beforehand.

What ou aim to do is quite unclear. Could you try to explain it algebrically ?

@EmmanuelCharpentier The accepted answer is exactly what I wanted to do.