Answer Happy

15. Let (11, 12,..., In) be independent samples from the uniform distribution on (1,6). Let Xin) and X 1) be the maximum and minimum order statistics respectively, (a) Show that 2nYn xã where Y = - In () 0-1 X(n)-1 (b) Show that 2 Į (-1) x In i=1
13. A random sample (21, 22, ...,2m) of size m is taken from a normal population with unknown mean y and variance o?. The mean is estimated from the all observations but, the variance is estimated from the first n observations only (n < m). Let Em 4 and s= (2-3)? m TE 72 i=1 (a) state the sampling distribution of 2 and (Em - # (b) Find the distribution of T Sn min-1)
14. Let (11, 12,..., In) be independent samples from the population with distribution described by the density function f(1) = 0e-82–8), r > (a) Find the distribution of Sri-nB. 12 (b) Find the mean and variance of (c) Show that X(1) - B is exponentially distributed and clearly specify its parameter, X(1) is the minimum order statistic. (d) Hence write a function of X(1) – 3 that is distributed as the chi-square and specify its degrees of freedom.