for-t-gt-0-and-f-t-4pit-n-2-e-x-2-4t-prove-that-R-f-t-x-dx-1-t-gt-0-

Question Number 29028 by abdo imad last updated on 03/Feb/18

f o r t > 0 a n d f (t) = {(4 π t)}^{- \frac{n}{2}} e^{- \frac{x^{2}}{4 t}} p r o v e t h a t

\int_{R} f_{t} (x) d x = 1 \forall t > 0 .