Specify initial evaluation points [Feature Req.]

For DiffEqUncertainty expectation() applications, distributions that are narrow relative to the support can lead to incorrect results via Quadrature as the integrand is not sampled at points w/ non-zero (numerically) joint pdf values.

B/c we know the pdf, it would advantageous to "seed" or initialize any adaptive quadrature methods w/ the mean and/or random samples from the distribution.

E.g. for a simple linear system, u'=p*u, with uncertain IC,

u0_dist = [truncated(Normal(3.0,2.0),-1000,1000)]

will produce expectations of 0

while

u0_dist = [truncated(Normal(3.0,2.0),3-1000,3+1000)]

produces the correct result. The reason being that the midpoint of the integration domain is used as initial quadrature points in most algorithms supported.

Start at the expectation() entry point used by DiffEqUncertainty and trace how adaptive quadrature methods choose their initial points. Reproduce the narrow truncated-Normal example from the issue, then determine how mean or random samples can seed the integration. Done means the narrow-support case produces the correct expectation without regressing existing quadrature behavior.