If you can, add a legend, to help distinguish between the three time series.

Hints:

```{hint}

:class: dropdown

* If you call the `plot()` function multiple times before calling `show()`, all of the lines you produce will end up on the same figure.

* For the legend, noted that if `var = 42`, the expression `f'foo{var}'` evaluates to `'foo42'`.

Note: `f'foo{var}'` is an example of [f-String](https://docs.python.org/3/tutorial/inputoutput.html#tut-f-strings), which allows you to use `{}` to contain an expression. The contained expression will be evaluated, and the result will be placed into the string.

```

```{exercise-end}

plt.show()

```

```{note}

`f'$\\alpha = {α}$'` in the solution is an application of [f-String](https://docs.python.org/3/tutorial/inputoutput.html#tut-f-strings), which allows you to use `{}` to contain an expression.

The contained expression will be evaluated, and the result will be placed into the string.

```

```{solution-end}

```

import numpy as np

```

```{hint}

:class: dropdown

Your hints are as follows:

* If $U$ is a bivariate uniform random variable on the unit square $(0, 1)^2$, then the probability that $U$ lies in a subset $B$ of $(0,1)^2$ is equal to the area of $B$.

* If $U_1,\ldots,U_n$ are IID copies of $U$, then, as $n$ gets large, the fraction that falls in $B$, converges to the probability of landing in $B$.

* For a circle, $area = \pi * radius^2$.

```

```{exercise-end}

```