program drop _all

clear

pause on

set obs 5000

local i = 1
while `i' < 21{
gen z`i' = invnorm(uniform())
gen chi_`i' = z`i'^2
local i = `i' + 1
}

gen F_1 = chi_1/(chi_1 + chi_2 + chi_3 + chi_4 + chi_5 + chi_6 + chi_7 + chi_8 + chi_9 + chi_10)
graph F_1, bin(50) normal
pause
sum F_1, d