Poisson & Geometric Hypothesis Testing (Edexcel A-Level Further Mathematics): Flashcards

$\lambda$ (the mean of Poisson distribution)

$P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}$

Both equal $\lambda$

$H_0: \lambda = \lambda_0$ (specifies a value)

One-tailed ($\lambda > \lambda_0$ or $<$) or two-tailed ($\neq$)

Observed value of $X$ following $\text{Po}(\lambda)$

Probability of rejecting $H_0$ when $H_0$ is true

Range of $X$ values leading to rejection of $H_0$

$P(\text{Reject } H_0 | H_0 \text{ true}) \leq \alpha$

$\alpha/2$ in each tail