Question

大学概率论 证明相互独立设

Answer 1

应该是这样的

f_X(x)=∫[-无穷,无穷]f(x,y)dy

=∫[-无穷,无穷]1/(50pi)e^(-(x^2+y^2)/50)dy

=1/(根号(50pi))e^(-x^2/50)∫[-无穷,无穷]1/(根号(50pi))e^(-y^2/50)dy

=1/(根号(50pi))e^(-x^2/50)

同理f_Y(y)=1/(根号(50pi))e^(-y^2/50)

且f(x,y)=1/(50π) * e^[-(x^2+y^2)/50]=f_X(x)f_Y(y)

所以X,Y独立