1. Your friend makes the claim that when one has a sample of data Y1 , . . . , Yn iii U niforn1(3,1), the maximum datum I9 = Yl'} is an unbiased estimator of 3. You know this is a crazy statement, but you decide that perhaps you should compute the bias of this estimator anyway. (a) Derive the bias for the specic case n = 2 (i.e., the case where you have two random samples, Y1 and Y2). Use the fact that the pdf of the maximum Yin} of 73. samples from a distribution fy (y) is given by fch; (y) = Tifvlyllfyll'l. You can verify whether your expression makes sense by, e.g., plugging in the value I? = U: do you get the value 2/3? (b) New derive a general expression for the bias as a function of u, for any I?