1. Let Y1 <>Y2 < ·="" ·="">·<>Y5 be the order statistics of a random sample of size . 5 from the distribution having p.d.f. f( x) = exp [-(x - 9)/ P]jp, (J <>x <>oo, zero elsewhere. Discuss the construction of a 90 percent confidence interval for P if O is known.
2. Three independent random samples, each of size 6, are drawn from three normal distributions having common unknown variance. We find the three sample variances to be 10, 14, and 8, respecti vely.
(a) Compute an unbiased estimate of the common variance.
(b) Determine a 90 percent confidence interval for the common variance.