Hello, everyone.

Sorry, my LaTeX is working "part-time"

Let

X1 ~ U(0,1)

X2 ~ U(0,1)

X1 and X2 are independent.

Now, consider

x1 = 0.05

x2 = 0.05

Let:

Z =

Y =

W = Z+Y

where

W ~

In this case,

W = 7.814+3.841 = 11.656

Prob [ W> ] = 0.00209975 for an alpha level = 5%.

So, my question is:

Is there a way to create

Z =

Y =

where n and m are large numbers (say, n>100000) - so that

W ~ and

Prob [ W> ] is still equal (or approximately equal ) to 0.00209975 for an alpha level = 5%?