Question

Example 5.5 (Discrete case). Let X be a discrete random variable, r be its observation, and the pmf of X be given by 1 2345678 9 10 ac f (x:0) 0 0.58 0.02 0.05 0.03 0.11 0.01 0.07 0.04 0.09 f( 1) 0.6 0 0.06 0.08 0.03 0.01 0.04 0.12 0.02 0.04

Answer 1

Solution) $\alpha=$ Type I error = P(rejecting $H_0$ when $H_0$ is true)

Rejection region = $( x ; x \epsilon C=(1,7,3,8,4))$

When $H_0$ is true

$\alpha= 0+ 0.02+0.05+ 0.01+0.07=0..15$

$\beta$ = P(Accepting $H_0$ when H1 is true )

$\beta= 0+0.08+0.03+0.01+ 0.02=0.14$