Molecular communications. Suppose Alice wants to send one bit message (1 or 0) to Bob. If the message is 1, Alice emits molecules, which will be then detected by Bob. If the message is 0, Alice does not emit any molecule. Suppose that given Alice emits molecules, the number of molecules detected at Bob for t minutes, denoted by N(1), follows Poisson distribution N() Poisson(t). Assume that Alice emits molecules. Let T denote the time Bob waits until it detects the first molecule. Find the pdf of T.
