Standard deviation can be undefined when the variance integral diverges, which is common in certain probability distributions like the Cauchy distribution. In this case, the user provided a probability density function f(x) = 24/x^3 but did not specify any restrictions on x. The lack of valid constraints on x raises questions about the legitimacy of the density function. Without proper limits, the integral for calculating variance becomes undefined. Clarifying the domain of x is essential for determining the validity of the probability density function.
