高数概率论。这都<0了,怎么还跟0取交集??

2025-05-15 12:25:01
推荐回答(1个)
回答(1):

f(x,y)=(1/2)(x+y)e^(-(x+y) f(x) =∫[0到∞](1/2)(x+y)e^(-(x+y))dy = (1/2)∫[0到∞]xe^(-(x+y))dy + (1/2)∫[0到∞]e^(-(x+y))dy = (1/2)xe^(-x)∫[0到∞]e^(-y)dy + (1/2)e^(-x)∫[0到∞]ye^(-y)dy = (1/2)xe^(-x)+ (1/2)e^(-x) = (1/2)(1+x)e^(-x), x.