Assume that there is a 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.

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.

Assume that there is a 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))?

Assume that there is a 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.