Complex Analysis Answers

Decide whether these series is convergent or divergent .

1. Sum (n+i sin n ) ^ {1/n}
2 Sum ( n^{in} ) , where n ^ in is taken in the 3π-branch

Hint : If you wish,You can use the fact
lim Zn=0 <--> lim |Zn| = 0
as n approach to infinity

Let x(t) be a random process defined as X(t)=A.COS[2 pi.T+Theta],Where A is a Rayleigh distributed random variable with mean and variance E[A]=0.5,Variance A = 1 .The random variable theta is uniform distributed on the interval [-pi ,pi],which is statistically independent from A.

A. Compute E[X(t1) X(t2)],for t1=t2=3 , and t1=0.5, t2=2.5
B.is the process X(t)wide sense stationary ?justify your answer
C. Find fxt (xt).

Let x(t) be a random process defined as
x(t)=A COS [2 PI .T+ Theta],where A is a Gaussian random variable with mean E{A}=0 and variance A = 2, The random variable theta is uniform distributed on the interval [-pi,pi], which is statistically independent from A.
Define random process Z(t) given by
Z(t)=integral from 0 to 1 of X(t) dt

A. Compute the mean of Z(t), E[Z(t)]
b. Determine the variance of Z(t), vaiance z
c. Is the process Z(t) strict sense stationary ,wide sense stationary ? Justify your answer
D. Is the process X(t) Gaussian process ?