Most probable value vs maximum of the distribution Given a distribution p(x), there are two things that can be calculated.

*

*Value of x for which p(x) is maximum.

*Most probable value of x weighted over p(x).

Would these two values of x be the same?

The expected value and most probable value can but need not coincide. Consider a random variable $X$ defined by $P(X=0)=0.9$ and $P(X=1)=0.1$. The most probable value is $0$, yet the expected value is $0.1$.
If your idea of “most probable value weighted over the distribution” is the expected value, then, no, these values need not be equal.
