## is there evidence that the mean delivery time for the local pizza restaurant is less than the mean delivery time for the national pizza chain?

A local pizza restaurant and a local branch of a national chain are located across the street from campus. The local pizza restaurant advertises that they deliver to the dormitories faster than the national chain. In order to determine whether this advertisement is valid, you and some friends have decided to order 10 pizzas from the local pizza restaurant and 10 pizzas from the national chain. Thus you have matched (paired) samples. For each of the 10 times that pizzas were ordered, you have one measurement from the local pizza restaurant and one from the national chain. The delivery times in minute are show in table: Time 1 2 3 4 5 6 7 8 9 10 Local 16.8 11.7 15.6 16.7 17.5 18.1 14.1 21.8 13.9 20.8 Chain 22.0 15.2 18.7 15.6 20.8 19.5 17.0 19.5 16.5 24.0 At the 0.05 level of significance, is there evidence that the mean delivery time for the local pizza restaurant is less than the mean delivery time for the national pizza chain? (5) What assumption is necessary about the population distribution to perform this test in i) (2)

### Write the integral expression for the two-parameter output correlation function  over the time intervals .

Consider the following mean-square differential equation, driven by a WSS random process  with psd The differential equation is subject to the initial condition , where the random variable  has zero-mean, variance 5, and….

### Repeat the corresponding segment of the correlation function periodically.

If a stationary random process is periodic, then we can represent it by a Fourier series with orthogonal coefficients. This is not true in general when the random process, though….

### Show that an m.s. derivative process  exists here.

Certain continuous time communications channel can be modeled as signal plus an independent additive noise (a) The receiver must process  for the purpose of determining the value of the message random….