Suppose under the null hypothesis H, X ∼ p, where p(x) = P(X = x) = 1/20, x ∈ {1, 2, … 20} and under the alternative hypothesis K, X ∼ q where q(x) = P(X = x) = \(\rm\frac{x}{210}\), x ∈ {1, 2, … .20}. Define two test functions ϕ and ψ for testing H against K such that,

ϕ(x) = \(\begin{cases}1 & \text { if } \rm x \leq 2 \\ 0 & \text { otherwise }\end{cases}\)

and

ψ(x) = \(\begin{cases}1 & \text { if } \rm x \geq 19 \\ 0 & \text { otherwise. }\end{cases}\)

Which of the following statements are true?