For a transistor α and β are given as α = I _ C I _ E and β = I _ C...

In the case of the transistor the relation between emitter current, base current and, the collector current is, ${i}_{\text{E}} = {i}_{\text{B}} + {\text{i}}_{\text{C}}$, $⇒ \dfrac{{i}_{E}}{{i}_{C}} = \dfrac{{i}_{B}}{{i}_{C}} + 1$,

$⇒ \dfrac{1}{\alpha} = \dfrac{1}{\beta} + 1$

$⇒ \beta = \dfrac{\alpha}{1 - \alpha}$