Correction Exercice 2 ECO-2025N

#رياضيات#تعليم
xix_i012
p(X=xi)p(X = x_i)......18\dfrac{1}{8}38\dfrac{3}{8}

1/

p(X=0)+18+38=1  ⟹  p(X=0)=48=12\begin{align*} &p(X=0)+\dfrac{1}{8}+\dfrac{3}{8}=1 \\ &\implies p(X=0)=\dfrac{4}{8}=\dfrac{1}{2} \end{align*}

2/

E(X)=∑k=0k=2k.p(X=k)=0×12+1×18+2×38=78\begin{align*} E(X)&=\sum_{k=0}^{k=2} k.p(X=k)\\ &=0\times\dfrac12+1\times\dfrac18+2\times\dfrac38\\ &=\dfrac78 \end{align*}