, be an arbitrary example trom a Weibull dissemination X

, w WEI(B, 2).

Q = 2 x2(2n).

(a) Show that

1-1

(b) use Q to infer an equivalent followed 10/0/0 certainty stretch peak e.

(c) Find a lower 100/0/0 certainty limit peak t) exp[ - (t19)2]

(d) Find an upper 100/0/0 certainty limit peak the ptn percentile of the circulation.

62..

Assume a crate contains visit marbles, e white ones and 4 - 9 dark ones. Test Ho: e = 2 against

Hs: 9 2 as follows: Draw two marbles witn substitution and reject Ho it botn marbles are the

same tone; in any case don't dismiss

(a) Compute the likelihood ot Type I blunder.

(b) Compute the likelihood ot Type II blunder pinnacle every conceivable circumstance.

(c) Rework (a) and (b) if the two marbles are drawn without substitution

63..

Consider an appropriation witn pdf t(x: 9) = exs-I it O < x < 1 and zero otnemise.

(a) Based on an arbitrary example of size n 1, track down the most impressive test ot Ho: e - 1 against Hs

witna=o.05_

(b) Compute the force ot the test in (a) pinnacle the elective 9 = 2.

(c) Derive the most impressive test peak the speculations ot (a) in light of an arbitrary example ot size n.

64..

Let Xl, be an irregular example trom a typical dispersion X

(a) Find an UMP test ot Ho: = against Hs: u <

(b) Find an UMP test ot Ho: = against Hs: u >

(c) Show that there is no LIMP test ot Ho = g against I-is: