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1. It is known that a random variable X has a Poisson distribution with parameter µ. A sample of 200 observations from this population has a mean equal to 3.4. Construct an approximate :90 percent confidence interval for µ.

2. Let Y1 Y2 ··· Y,. denote the order statistics of a random sample of size n from a distribution that has p.d.f. f( x) = 3:x:2/fJ3, 0 x 8, zero elsewhere.

(a) Show that Pr (c Y,./8 1) = 1 - &11, where O c 1.

(b) If n is 4 and if the observed value of Y4 is 2.3, what is a 95 percent confidence interval for 8?

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