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?

No.
To make it easier for comprehension, we may consider the discrete case, where 'p(x) is maximum' refers to the event that takes place most, while 'Most probable value of x weighted over p(x).' (expectation) refers to the average value. In a extreme case if you have a dice with four '0's and two '1's, the value of x for which p(x) is maximum is clearly $0$ and the most probable value of x weighted over p(x) is $1/3$, which is even not a value you would ever see in any cases.
Also, it's actually a bit confusing when you say "Most probable value of x weighted over p(x)", for the term "Most probable value" itself means value of x for which p(x) is maximum. I guess you are trying to refer to the expectation.
