probability or statistics – White Noise Process with asymmetrical Uniform Distribution

I can evaluate the Mean of the following White Noise Process successfully returning $0$:

Mean(WhiteNoiseProcess(UniformDistribution({-1, 1}))(t))

Using an Uniform distribution in any symmetric interval of the form $(-a, ,a)$ evaluates OK, but I can not use an asymmetric interval, thus the following:

Mean(WhiteNoiseProcess(UniformDistribution({0, 1}))(t))

stays unevaluated. Is this a bug? Or, am I missing something?