(a) Explain the notions of a type I and type II error. Why does one increase when...

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(a) Explain the notions of a type I and type II error. Why does one increase when the other decreases?

(b) How does the Neyman-Pearson procedure solve the problem of a trade off between the type I and type II errors?

(c) Compare and contrast the power of a test at a point, and the power function.

(d) What do we mean by a uniformly most powerful test?

(e) Explain the concepts of (i) unbiased test and (ii) consistent test.

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