Hi,

I have a question reagrding the normal distribution.

Suppose there are 3 normal distribution equations as follows

X1~N(5,9)

X2~N(10,16)

X3~N(5+10,9+16)

And I used Excel to generate random numbers for different normal distributions.

Then I found that the sum of X1+X2 equals X3.

Can anyone please explain me why X1+X2 equals X3?