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Poisson 1then Tn: In other words, Xn con- verges in distribution to zero, which implies convergence in probability to zero.

Here is the plot: Similarly, as a function of x, fX Y Soluions x y, z is an N y, 1 density. It just remains to compute the quantities used in the formulas. We must show that B is countable. Observe that g is a periodic sawtooth function with period one.

Since gn Y converges, it is Cauchy. Observe that Xn takes only the values n and zero.

## Frame ALERT!

Before proceeding, we make a few observations. R Let Pn t denote the above integral. There are 52 14 possible hands.

Since this depends on t1 and t2 only through their difference, we see that Yt is WSS if Xt so,utions second-order strictly stationary.

Chapter 11 Problem Solutions Let W denote the event that the decoder outputs the wrong message. If all An are countable, then n An is also countable by an earlier problem. Let R denote the number of red apples in a crate, and let G denote the number of green apples in a crate. Hence, they are uncorrelated.

The player wins if any of the 4! In order that the first header packet to be received is the 10th packet to arrive, the first 9 packets gubnsr be received must come from the 96 data packets, the 10th packet must come from the 4 header packets, and the remaining 90 packets can be in any order.

Since SX f is equal to its complex conjugate, SX f is real.

If the function q W: We have from the example that with p: Thus, if Z is circularly symmetric, so is Solutiins. If two disjoint events both have positive probability, then they cannot be independent. This is a causal impulse response.

It is obvious that the Xi are zero mean. Let O denote the event that a cell is overloaded, and let B denote the event that a call is blocked. Hence, by Prob- lem 55 c in Chapter 4 and the remark following it, 2 Z 2 is chi-squared with two degrees of freedom. Let Xk denote the number of coins in the pocket of the kth student.

Consider the i j component of E[XB]. Sim- ilarly, as a function of y, fY Z y z is an N z, 1 density.

### Errata for Probability and Random Processes for Electrical and Computer Engineers

To find the Chernoff bound, we must minimize h s: Since U, Vand W are i. Using only the numbers 1, 2, 3, 4, 5, 6, consider how many ways there are to write the following numbers: We again hubner 1 and 2 to be the defective chips. We first point out that this is not a question about mean-square convergence.