Question: Suppose that a single observation X is to be drawn from the following p.d.f.: where the value of is unknown (0

Suppose that a single observation X is to be drawn from the following p.d.f.:

where the value of Î¸ is unknown (0 ‰¤ Î¸ ‰¤ 2). Suppose also that the following hypotheses are to be tested:
H0: Î¸ = 2,
H1: Î¸ = 0.
Determine the test procedure Î´ for which Î±(Î´) + 2Î²(Î´) is a minimum, and calculate this minimum value.

rum ={2(1-e" +. otherwise.

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