fx(x)是f(x)的密度函数
fy(y)=2fx(根号(4-y))|dx/dy|=fx(根号(4-y))/根号(4-y)
e^[(y-4)/2]/[根号(pi(8-2y))sigma^2]好人做到底吧
是求大F换底求导FY(y)=P(Y=根号(4-y))+P(X(4-(4-y)~4-无穷)(负无穷~-根号(4-y))->(4-无穷~4-(4-y))FY(y)=∫(y~负无穷)f(x)(-1/(2根号(4-y))dy+∫(负无穷~y)f(x)(1/(2根号(4-y))dy=∫(负无穷~y)f(x)/(2根号(4-y))dy+∫(负无穷~y)f(x)(1/(2根号(4-y))dy=∫(负无穷~y){f(x)/(2根号(4-y))+f(x)/(2根号(4-y))}dy=∫(负无穷~y){f(x)/根号(4-y)}dy根据y求导,自然得到fY(y)=dFY(y)/dy=f(x)/根号(4-y)(y