Replicability of RandomVariate within a function?

Question

I have a rather basic question but can't figure out a foolproof answer. In the following code, I build a function which returns the mean difference between successive elements of a vector created from j random variates from an exponential distribution:

fun2[j_] := 
    Module[{x = RandomVariate[ExponentialDistribution[1/25], j]}, 
    Mean[Table[Abs[x[[i + 1]] - x[[i]]], {i, Length[x] - 1}]]]

Will the use of the x call to RandomVariate create an immutable object, i.e. so that x[[i + 1]] and x[[i]] reference the same instance of the distribution?

Thanks a lot for any help.

Answer 1

Yes. Notice that performing the computation outside of the Module produces the same result.

SeedRandom[1];
fun2[10]

(* 30.5828 *)

SeedRandom[1];
x = RandomVariate[ExponentialDistribution[1/25], 10];
Mean[Abs[Differences[x]]]

(* 30.5828 *)

In order to get the undesired behavior you would use SetDelayed as such..

fun3[j_] := 
 Module[{x := RandomVariate[ExponentialDistribution[1/25], j]}, 
  Mean[Table[Abs[x[[i + 1]] - x[[i]]], {i, Length[x] - 1}]]]

This gives a totally different result.

SeedRandom[1];
fun3[10]

(* 34.018 *)