6.4.19. A sample of size 1is taken from the geomctric probability model, *px** **(k**)** *= (1 - p)k-l *p, **k** *= 1. 2, 3, . .., to test *Ho:** **p** *= lversus H1: *p** *> !·The null hypothesis is to be rejected if *k** *.?: 4. What is the probability that a Type II error will be committed when *p** *= 1?

6.4.20. Suppose that one observation from the exponential pdf, *f y(y **) *= *)..e-/..y **. **y *> 0, is to be used to test Ho: " = 1 versus H1 : *>.. * 1. The decision rule calls for the null hypothesis

to be rejected if *y *:?:. In 10. Find *fJ *as a function of "-·

6.4.21. A rnndom sample of size 2 is drawn from a uniform pdf defined over the interval [O, B].

We wish to test

Ho:8 = 2

versus

*H1: B * 2

by rejecting *Ho *when YI + Y2 *s **k . *Find the value *for k *that gives a level of significa nce of0.05.

6.4.22. Suppose that the hypotheses of Question 6.4.21 are to be tested with a decision rule of the form, "Reject *Ho: B *= 2 if YtY2 ::: *k* **."** *Find the value of *k" *tha t gives a level of

significance of 0.05 (see Theorem 3.8.3).

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