Question

A stationary random process X(t) is applied to the input of a system for which h(t) = u(t) t^2 e^(-8t). If E[X(t)] = 2, the mean value of the system’s response Y(t)  is

(a) 1/128

(b) 1/64

(c) 3/128

(d) 1/32

I had been asked this question during a job interview.

Query is from Random Process in division EDC Overview of Electronic Devices & Circuits

Answer 1

Correct option is (c) 3/128

Easiest explanation: The mean value of Y(t) is integral of h(t)dt over negative infinity to positive infinity which gives the value equal to 3/128.