So say you rate interval is policy year interval for those classified x nearest on policy anniversary.

and you are now told that birthdays occur on average 1/6 years after the policy anniversary on which they were x nearest.

Normally the formula to calculating exposure is 1/2 ( Px(t) + Px(t+1) ) [assuming Px(t) is linear]

From what I think, it changes to 1/2 (Px(t) + Px-1(t+1))

May someone explain to me why I am right or wrong?