Transistor numbers in code

You will write four functions that a designer uses for a transistor in the common-emitter circuit.

The idea. $\beta = \dfrac{\alpha}{1 - \alpha}$. In a circuit with one supply, $I_B = \dfrac{V_{CC} - 0.7}{R_B}$, $I_C = \beta I_B$ and $V_{CE} = V_{CC} - I_C R_C$, as long as the transistor is active. The collector voltage cannot go below $0.2$ V.

Your tasks.

1. In beta_from_alpha, return $\beta$ for a given $\alpha$.
2. In collector_voltage, return $V_{CE}$ in V for a supply vcc, a base resistor rb, a collector resistor rc and a current gain beta, as if the transistor were active.
3. In region, return "saturated" if the $V_{CE}$ of task 2 is below $0.2$ V and "active" otherwise.
4. In voltage_gain, return the size of the gain $\dfrac{\beta R_C}{r_i}$.