概率论知识回顾（十四）：离散与连续随机变量的期望

f ( x ) = { β α Γ ( α ) x α − 1 e − β x x ; 0 0 x ≤ 0 f(x) = \begin{cases} \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha -1}e^{-\beta x} ; x ; 0 \\ 0 ; x \le 0\end{cases} f(x)={Γ(α)βα​xα−1e−βx0​x>0x≤0​

Γ ( α ) = ∫ 0 + ∞ t α − 1 e − t d t \Gamma(\alpha) = \int_{0}^{+\infty}t^{\alpha-1}e^{-t}dt Γ(α)=∫0+∞​tα−1e−tdt

E ( X ) = α β E(X) = \frac{\alpha}{\beta} E(X)=βα​