There's an intuition in me that whenever I look at a graph of a random variable's graph, its expected value should be that specific $x$ that has the maximum function value. That was the case at `normal` distribution. But I encoutnered other distributions, like the `gamma` distribution, and it wasn't always the case with that. I read a Wikipedia that is has the expected value of $k\theta$ and for like $k = 2$ and $\theta=5$ case, the corresponding expected value would be $10$, but the function has its maximum value at around $5$.

I thought the density function says how probable certain values are, although the value not displaying its probability of course, but where the function has bigger values, the probability also goes higher. For example: sampling a random variable, then looking at the sample's histogram clearly shows that more numbers were generated near points where the function had bigger values. Also, I thought the expected value names the value which is the most likely to be drawn of a random variable. So I had a general intuition that where the function has its maximum value, that's what its expected value is.