How can you use the sample median Y' to prove consistency?
If 2n+1 random observations are drawn from a continuous and symmetric pdf with mean (mu) and if f_Y(mu;mu) does not equal 0, then the sample median Y'_(n+1), is unbiased for (mu) and Var( Y'_(n+1) ) = 1/8[ f_Y(mu;mu)^2 *n ]. Show that (mu) hat = Y'_(n+1) is consistent for (mu).