Given : rejection region = {X | X is an integer }
P[Type I error ]= Probability of rejecting H0 when H0 is actually true
=P[ X is an integer | X ~ N(5,4) ] =
The normal curve is between , so betwwen this interval there will be all the integers included. But each integer will be a point on the axis and area corresponding to each of these points will be nearly 0. So, sum of
P[Type II error] = Probability of accepting H0 when H0 is false
= P[X is an integer | X ~ bin(25,0.2) ]= 1
since, all of X's realisations are natural numbers and hence, integers.
3. You will have just a single observation of X on which to base your choice...
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