A store sells strings by length. The price is 1 SEK/m. It is more common that customers buy shorter strings than longer, the sales follows an exponential distribution with parameter λ.
There is however a problem. The cash register, a very special machine with infinite precision, has a hardware problem with the N:th bit. When customers pay, it flips with probability p.
A customer can therefore end up with paying 2^N more or less than what was intended.
What is the expected price change?