随机变量X与Y相互独立,X的分布 1 2 3 0.3 0.2 0.5 Y的密度函数为f（y）,求U=X+Y的密度函数

f(u)=f(y)+0.3 x=1
=f(y)+0.2 x=2
=f(y)+0.5 x=3
因为x和y是独立的,f（x+y)=f（x）+f（y）

f_u(u)=f(y=u-3 and x=3) + f(y=u-2 and x=2) + f(y=u-1 and x=1)
since X and Y are independent,
f(y=u-i and x=i)=f_y(y=u-i)*p(x=i)=f_y(u-i)*p(x=i), where i=1,2,3.
So
f_u(u)=f_y(u-3)*p_x(x=3)+f_y(u-2)*p_x(x=2)+f_y(u-1)*p_x(x=1)
=f(u-3)*0.5 + f(u-2)*0.2 + f(u-1)*0.3

mm