The pmf of a random variable X is given below.

x 1 2 3 4 5
p(x) .1+Ѳ .2+Ѳ .2 + 3 Ѳ .1- Ѳ .4 - 4 Ѳ
In a test H_0: Ѳ = 0 versus H_1 : Ѳ = .1, H_0: is rejected if X=1 , X=2 or X=3.
a) what is the probability of a type I error.
b) is this a powerful test?

Question

The pmf of a random variable X is given below.

x	1	   2	     3	               4	       5
p(x) 	.1+Ѳ  .2+Ѳ   .2 + 3 Ѳ   .1- Ѳ      .4 - 4 Ѳ
In a test H_0: Ѳ = 0 versus H_1 : Ѳ = .1, H_0: is rejected if  X=1 , X=2 or X=3. 
a) what is the probability of a type I error. 
b) is this a powerful test?

anonymous · Answer

P(type I error) = Probability of rejecting H0 when it's true.

this would be P(X=1|H0)+P(X=2|H0)+P(X=3|H0)

anonymous · Answer

power is probability of rejecting when H0 is false.

this would be P(X=1|H1)+P(X=2|H1)+P(X=3|H1)

anonymous · Answer

you there?

anonymous · Answer

@leenagorgeous

anonymous · Answer

thanks. that make sense. Can you solve it further more please?

anonymous · Answer

all you have to do is calculate the probabilities!  

hint:
P(X=1|H0) =.1 + $\theta$  but if H0 is true, then $\theta=0$, so 
P(X=1|H0) =.1 + 0 = .1

does that make sense?