68. Let X represent a measurement error of some sort. It is natural to assume that the pdf f (x) is symmetric about 0, so that the density at a value c is the same as the density at c (an error of a given magnitude is equally likely to be positive or negative). Consider a random sample of n measurements, where n2k
1, so that Yk1 is the sample median.What can be said about E(Yk1)? If the X distribution is symmetric about some other value, so that value is the median of the distribution, what does this imply about E(Yk1)?
Hints: For the rst question, symmetry implies that 1F(x)P(X x)P(Xx)F(x). For the second question, consider ; what is the median of the distribution of W?