In Section 13.4 we described how the probability density function could be recovered from a sequence X 1 , X 2 , X 3 , XXXXXXXXXXWe consider the Gam(2, 1) probability density discussed in the main...

In Section 13.4 we described how the probability density function could be recovered from a sequence X₁, X₂, X₃, . . . . We consider the Gam(2, 1) probability density discussed in the main text and a histogram bar around the point a = 2. Then f(a) = f(2) = 2e−2 = 0.27 and the estimate for f(2) is Y¯n/2h, where Y¯n as in (13.3)

a. Express the standard deviation of Y¯n/2h in terms of n and h

b. Choose h = 0.25. How large should n be (according to Chebyshev’s inequality) so that the estimate is within 20% of the “true value”, with probability 80%?