Suppose that $X$ is a random variable with PDF $f(x)$ with support $(-\infty,\infty)$. Suppose that the expectation of $X$ is $\mathbb{E}(X)=\lambda$.
Is it always true that
$$\int_{-\infty}^{\lambda} f(x)dx = \frac{1}{2}$$ $$\int_\lambda^{\infty}f(x)dx = \frac{1}{2}$$