Creating a list of $xy$ pairs

Question

How do I create a list of $xy$ pairs of points where the $x$ points are evenly spaced between a given range with a specific step size, and the $y$ points are given by a function, but with some random noise added from a normal distribution with mean $= 0$ and standard deviation $= 1$ if I am given the function?

Answer 1

A standard way would probably be

Table[{x, f[x] + RandomVariate[NormalDistribution[]]}, {x, x0, x1, dx}]

for x in steps of dx in the range x0 to x1, inclusive.

Answer 2

x = Range[1, 20, .3];

y = #^2 + RandomVariate[NormalDistribution[]] & /@ x;

Transpose[{x, y}]