(Two models of information transfer) Consider a random variable whose value is transmitted.
(a) Suppose that the variable has standard deviation n and that the true value is transmitted with noise of standard deviation 1. What is the amount of information transmitted?
(b) Alternatively, suppose that the variable has n equally probable values, and the actual value is transmitted exactly. How much information is transmitted?
(c) As n → ∞, how do these values compare?