Question
We define the following random variables. Y is such that P(Y=−3)=0.3 and P(Y=7)=0.7. Z follows a binomial law with parameters 6, 0.8 E(Y)= E(−7Y)= E(Y+Z)=
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Answer to a math question We define the following random variables. Y is such that P(Y=−3)=0.3 and P(Y=7)=0.7. Z follows a binomial law with parameters 6, 0.8 E(Y)= E(−7Y)= E(Y+Z)=
Timmothy
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Pour calculer l'espérance mathématique d'une variable aléatoire discrète, on utilise la formule suivante :
E(X) = \sum_{i} x_i \cdot P(X=x_i)
où x_i P(X=x_i)
1. Calcul de E(Y):
E(Y) = (-3) \cdot P(Y=-3) + 7 \cdot P(Y=7)
E(Y) = (-3) \cdot 0.3 + 7 \cdot 0.7 = -0.9 + 4.9 = 4
2. Calcul de E(-7Y):
E(-7Y) = -7 \cdot E(Y) = -7 \cdot 4 = -28
3. Calcul de E(Y+Z):
E(Y+Z) = E(Y) + E(Z)
Pour Z suivant une loi binomiale de paramètres 6, 0.8, on a que l'espérance de Z est np n = 6 p = 0.8
E(Z) = 6 \cdot 0.8 = 4.8
Donc,
E(Y+Z) = E(Y) + E(Z) = 4 + 4.8 = 8.8
\textbf{Answer:}
1. E(Y) = 4
2. E(-7Y) = -28
3. E(Y+Z) = 8.8
où
1. Calcul de E(Y):
2. Calcul de E(-7Y):
3. Calcul de E(Y+Z):
Pour Z suivant une loi binomiale de paramètres 6, 0.8, on a que l'espérance de Z est
Donc,
1.
2.
3.
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