A single observation of a random variable having a uniform density with 0 is used to test the null hypothesis 0 against the alternative hypothesis 0 2 If the null hypothesis is rejected if and only if the random variable takes on a value greater than 0 1, find the probabilities of type I and type II errors

Question: A single observation of a random variable having a uniform density with = 0 is used to test the null hypothesis = 0

A single observation of a random variable having a uniform density with α = 0 is used to test the null hypothesis β = β0 against the alternative hypothesis β = β0 + 2. If the null hypothesis is rejected if and only if the random variable takes on a value greater than β0 + 1, find the probabilities of type I and type II errors.

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