Suppose X(t) is a Gaussian random process with a mean E[X(t)] = 0 and autocorrelation function RXX() = e|| . Assume that the random variable

Suppose X(t) is a Gaussian random process with a mean E[X(t)] = 0 and autocorrelation function RXX(τ) = e−|τ|

. Assume that the random variable A is defined as follows:

A =

 B 0

X(t)dt where B is a uniformly distributed random variable with values between 1 and 5 and is independent of the random process X(t). Determine the following:

a. E[A]

b. σ2 A