Statistic nd probability inference

Question 3 Let X > 0 denote a continuous random variable taking only positive values with pdf f(x). (a) If f(x) > 0, VER+ argue that the median of X must be unique [ HINT: The cdf F(m) = 0.5 only at x = m Hence x = m + h for any h # 0 ? ] (b) Use a proof by contradiction to show that lim,- f (x) = 0 [HINT: Assume f(x) =0, Vx>0 what happens? ] (c) Let X ~ Exp(X) so the pdf of X is: f(x) = de-xx For what value of A will X have a x'(r) distribution and with what r