Edit
Here is a Mathematica one-liner, courtesy of ciao, that does what you ask for:
SeedRandom[42];
Array[(x[#] = RandomReal[1]) &, 10];
Definition @ x
x[1] = 0.425905
x[2] = 0.391023
x[3] = 0.347069
x[4] = 0.453741
x[5] = 0.555963
x[6] = 0.289169
x[7] = 0.296848
x[8] = 0.206408
x[9] = 0.32517
x[10] = 0.973325
And here is another one, producing non-indexed variables.
SeedRandom[42];
MapThread[Set, {Symbol["x" <> #] & /@ IntegerString[Range[10]], RandomReal[1, 10]}];
List @@ OwnValues /@ Hold[x1, x2, x3, x4, x5, x6, x7, x8, x9, x10]
{{HoldPattern[x1] :> 0.425905}, {HoldPattern[x2] :> 0.391023},
{HoldPattern[x3] :> 0.347069}, {HoldPattern[x4] :> 0.453741},
{HoldPattern[x5] :> 0.555963}, {HoldPattern[x6] :> 0.289169},
{HoldPattern[x7] :> 0.296848}, {HoldPattern[x8] :> 0.206408},
{HoldPattern[x9] :> 0.32517}, {HoldPattern[x10] :> 0.973325}}
Evaluate @ Array[x, 10] = RandomReal[1, 10]
doesn't float your boat? $\endgroup$ – J. M.'s ennui♦ Aug 20 '15 at 20:40