Question

概率密度,求函数那位大侠帮下P{0

Answer 1

如果设U = 3 - x,那么有 dU = -dx.因此

/ 1/9 (3-x)^2 dx = -(/ 1/9 U^2 dU) = -1/27 U^3 + C = -1/27 (3 - x)^3 + C

用定积分就是

/0^2 1/9 (3-x)^2 dx = (-1/27 (3 - x)^3)|0^2 = -1/27 + 1 = 26/27

总之设了一个u = u(x)之后就要算出du = du(x),然后分别代入求解就行了.