5. Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1-a)% confidence interval for B.

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5. Suppose that a random sample X₁, X2, X20 follows an exponential distribution with
parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1-x)%
confidence interval for B.
6. Suppose that a random sample X is given by a probability density function
- f = 10
(B-2), 0<x<B
0, otherwise
Without using MGF technique, prove or disapprove that is a pivotal quantity
f(x) = B²
Transcribed Image Text:5. Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1-x)% confidence interval for B. 6. Suppose that a random sample X is given by a probability density function - f = 10 (B-2), 0<x<B 0, otherwise Without using MGF technique, prove or disapprove that is a pivotal quantity f(x) = B²
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