# Question: In this exercise a proof of equation 7 73 is constructed

In this exercise, a proof of equation (7.73) is constructed. Write the random sum as

Where is a Bernoulli random variable in which Yi = 1 if N ≥ i and Yi = 0 if .

(a) Prove that Yi and are Zi independent and hence

(b) Prove that the equation of part (a) simplifies to

Where is a Bernoulli random variable in which Yi = 1 if N ≥ i and Yi = 0 if .

(a) Prove that Yi and are Zi independent and hence

(b) Prove that the equation of part (a) simplifies to

## Answer to relevant Questions

Suppose that Xk is a sequence of IID Gaussian random variables. Recall that the sample variance is given by (a) Show that the sample variance can be written as a quadratic form ŝ2 = XTBX and find the corresponding form of ...Find the variance of the sample standard deviation, Assuming that the Xi are IID Gaussian random variables with mean μ and variance σ2. Show by example that the random process Z (t) = X (t) + Y (t) may be a wide sense stationary process even though the random processes X (t) and Y (t) are not.Let and be independent, wide sense stationary random processes ...Let Wn be an IID sequence of zero- mean Gaussian random variables with variance . Define a discrete- time random process, X[ n] = pX[ n – 1]+ Wn, n = 1, 2, 3, … where X[ 0] = W0 and is a constant. (a) Find the mean ...Let, Xk , k = 1,2,3,…., be a sequence of IID random variables with mean and variance . Form the sample mean process σ2x.From the sample mean process (a) Find the mean function, µS [n] = E [S [n]]. (b) Find the ...Post your question