"A method that is easier to understand and does not make use of the $\\sin$ function is based on the fact that if $X\\sim U(0,1)$ and $Y\\sim U(0, 1), then $P[X^2+Y^2\\leq 1]=\\p/4$ (see [\"Monte Carlo method\"on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
"The data on the incidence of influenza-like illness are available from the Web site of the [Réseau Sentinelles](http://www.sentiweb.fr/). We download them as a file in CSV format, in which each line corresponds to a week in the observation period. Only the complete dataset, starting in 1984 and ending with a recent week, is available for download."
"Starting from this list of weeks that contain August 1st, we obtain intervals of approximately one year as the periods between two adjacent weeks in this list. We compute the sums of weekly incidences for all these periods.\n",
"\n",
"We also check that our periods contain between 51 and 52 weeks, as a safeguard against potential mistakes in our code."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"year = []\n",
"yearly_incidence = []\n",
"for week1, week2 in zip(first_august_week[:-1],\n",
