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## Homework Statement

Given that X is a uniform random variable on the interval [tex](0, \theta)[/tex], we might test [tex]Ho: \theta = 1[/tex] versus the alternative [tex]H_{1}: \theta = 2[/tex] by taking a sample of 2 observations of X and rejecting Ho if [tex]\bar{X} > 0.99[/tex]. Compute [tex]\alpha[/tex]

**2. The attempt at a solution**

[tex]\alpha[/tex] = P[type I error]

= P[rejecting Ho| Ho is true]

= P[[tex]\bar{X} > 0.99 given that \theta = 1][/tex]

I just know that if X is a uniform random variable, it has a pdf:

[tex]f\left(x; a, b\right) = \frac{1}{b - a}I_{[a, b]}(x)[/tex]

Kindly help me what to do next.