# Question

In Example 6b, let S denote the signal sent and R the signal received.

(a) Compute E[R].

(b) Compute Var(R).

(c) Is R normally distributed?

(d) Compute Cov(R, S).

Example 6b

Suppose that if a signal value s is sent from location A, then the signal value received at location B is normally distributed with parameters (s, 1). If S, the value of the signal sent at A, is normally distributed with parameters (μ, σ2), what is the best estimate of the signal sent if R, the value received at B, is equal to r?

(a) Compute E[R].

(b) Compute Var(R).

(c) Is R normally distributed?

(d) Compute Cov(R, S).

Example 6b

Suppose that if a signal value s is sent from location A, then the signal value received at location B is normally distributed with parameters (s, 1). If S, the value of the signal sent at A, is normally distributed with parameters (μ, σ2), what is the best estimate of the signal sent if R, the value received at B, is equal to r?

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