Suppose that F(x) has the following (scale-perturbed) form: where is the standard normal distribution function Show that F does not have a density function at θ, although the right-hand side and...

Suppose that F(x) has the following (scale-perturbed) form:

where is the standard normal distribution function Show that F does not have a density function at θ, although the right-hand side and left-hand side derivatives exist at 0. Verify that the median of F is still uniquely define and the sample median converges a.s. to the population median, as n → ∞. What can be said about the asymptotic law for