2 Let p(x) ~ U(0, a) be uniform from 0 to a, and let a Parzen...
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2 Let p(x) ~ U(0, a) be uniform from 0 to a, and let a Parzen window be defined as (x) = ex for > 0 and 0 for x ≤0. (a) Show that the mean of such a Parzen-window estimate is given by Pn(x)= { 0 (1-e-/hn) (ea/hn - 1)e-/hn x<0 0 ≤ x ≤a a≤r. (b) Plot Pn(x) versus x for a = 1 and h₂ = 1, 1/4, and 1/16. (c) How small does h₂ have to be to have less than one percent bias over 99 percent of the range 0 < x <a? Activate Windows (d) Find hn for this condition if a = 1, and plot p(x) in the range 0 <0.05 vate Windows. 2 Let p(x) ~ U(0, a) be uniform from 0 to a, and let a Parzen window be defined as (x) = ex for > 0 and 0 for x ≤0. (a) Show that the mean of such a Parzen-window estimate is given by Pn(x)= { 0 (1-e-/hn) (ea/hn - 1)e-/hn x<0 0 ≤ x ≤a a≤r. (b) Plot Pn(x) versus x for a = 1 and h₂ = 1, 1/4, and 1/16. (c) How small does h₂ have to be to have less than one percent bias over 99 percent of the range 0 < x <a? Activate Windows (d) Find hn for this condition if a = 1, and plot p(x) in the range 0 <0.05 vate Windows.
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