\textbf{Part A - First model}

Based on a data sample, we consider an initial modelling:
\begin{itemize}
  \item each year, the probability that the El Niño phenomenon is dominant is equal to 0.4;
  \item the occurrence of the El Niño phenomenon occurs independently from one year to the next.
\end{itemize}

We denote by $X$ the random variable which, over a period of 10 years, associates the number of years in which El Niño is dominant.

\begin{enumerate}
  \item Justify that $X$ follows a binomial distribution and specify the parameters of this distribution.
  \item a. Calculate the probability that, over a period of 10 years, the El Niño phenomenon is dominant in exactly 2 years.\\
b. Calculate $P ( X \leqslant 2 )$. What does this result mean in the context of the exercise?
  \item Calculate $E ( X )$. Interpret this result.
\end{enumerate}