Assume that there is a continuous random variable *x*, and its variance is var(*x*). Furthermore, there is a strictly monotonically increasing function *f*. Can anybody prove that the larger the var(*x*), the larger the variance of *f*(*x*), i.e. var(*f*(*x*))? One thing important is that the expectation of this random variable is fixed, with its variance to be the only part changeable.