Parametric model: (X , BX , Pθ), Pθ ∈ P = {Pθ|θ ∈ Θ}
where Θ = H0+˙ H1
X = K+˙ A : K: critical region = rejection region / A: acceptance
region
A decision rule d, where
d(x) =
dK , if x ∈ K
dA , if x ∈ A
is called a non randomised test. One tries to choose K in such a
way that
the number of wrong decisions becomes as small as possible. We
distinguish:
Type I error: H0 is correct, but is rejected (decision dK).
Type II error: H1 is correct, but decision for H0 (decision
dA).
If events A and B are not independent,
then the probability of the intersection of A and
B (the probability that both events occur) is defined
by
P(A and B) = P(A)P(B|A).
From this definition, the conditional probability P(B|A) is easily obtained by dividing by P(A):
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