1 Calculez l'espérance mathématique de chaque distribution. \[ \begin{array}{l} \text { a) } \Omega=\{-21,-13,4,15,26\} \\ P(-21)=27 \%, P(-13)=17 \%, P(4)=32 \% \\ P(15)=10 \%, P(26)=14 \% \end{array} \] b) \[ \begin{array}{l} \Omega=\{-20,-15 \\ P(-20)=\frac{3}{10}, \\ P(50)=\frac{1}{10} \end{array} \]

Step 1 ：First, we need to calculate the expected value for each distribution.

Step 2 ：For distribution a), we have the following formula: \(E(X) = \sum x_i P(x_i)\)

Step 3 ：So, \(E(X) = (-21)(0.27) + (-13)(0.17) + (4)(0.32) + (15)(0.10) + (26)(0.14)\)

Step 4 ：Calculating the sum, we get \(E(X) = -5.67 - 2.21 + 1.28 + 1.5 + 3.64 = -1.46\)

Step 5 ：For distribution b), we have the following formula: \(E(Y) = \sum y_i P(y_i)\)

Step 6 ：So, \(E(Y) = (-20)(\frac{3}{10}) + (50)(\frac{1}{10})\)

Step 7 ：Calculating the sum, we get \(E(Y) = -6 + 5 = -1\)

Step 8 ：Now, we have the expected values for both distributions: \(E(X) = -1.46\) and \(E(Y) = -1\)

Step 9 ：\(\boxed{E(X) = -1.46, E(Y) = -1}\)