확률밀도함수와 평균

$\displaystyle \int _{0} ^{1} f ( x ) dx = 1 \cdots \cdots \text{㉠}$ $\displaystyle \int _{0} ^{1} xf ( x ) dx = \frac{1}{4} \cdots \cdots \text{㉡}$ $\displaystyle 10 = \int _{0} ^{1} ( ax + 5 ) f ( x ) dx$ $\displaystyle = \int _{0} ^{1} axf ( x ) dx + \int _{0} ^{1} 5 f ( x ) dx$ $\displaystyle = a \int _{0} ^{1} xf ( x ) dx + 5 \int _{0} ^{1} f ( x ) dx$ $\displaystyle = \frac{1}{4} a + 5$ ($\because$ ㉠, ㉡에서) $\displaystyle \therefore \frac{1}{4} a = 5$ $\therefore a = 20$