Consider the formula below for estimating average delay d_i. Suppose that u = 0.2. Let r₁ t₁ be the most recent sample delay, let r₂ t₂ be the next most recent sample delay, and so on.

1. For a given audio application suppose four packets have arrived at the receiver with sample delays r₄ t₄, r₃ t₃, r₂ t₂, and r₁ t₁. Express the estimate of delay d in terms of the four samples.
2. Generalize your formula for n sample delays.
3. For the formula in Part b, let n approach infinity and give the resulting formula.
4. Comment on why this averaging procedure is called an exponential moving average. d_i = (1-u)d_(i-1) + u(r_i - t_i)