Question

For the system shown in the figure below, the input $X\left(t\right)$ is a stationary random process.

If the statistical mean value of the input process X(t) is 8, then the statistical mean value of the output process Y(t) will be ________

• A. 2

Answer 1

The correct option is A 2
For the given system,

$Y\left(t\right)=X\left(t\right)-3Y(t-T)E\left[Y\right(t\left)\right]=E\left[X\right(t)-3E[Y(t-T)]$

SInce the given system is LTI and input X(t) is a stationary process, the output Y(t)also will be a stationary process.

So, $E\left[Y\right(t-T\left)\right]=E\left[Y\right(t\left)\right]=\overline{Y}GiventhatE\left[X\right(t\left)\right]=\overline{X}=8\overline{Y}=\overline{X}-3\overline{Y}4\overline{Y}=\overline{X}\overline{Y}=\frac{\overline{X}}{4}=\frac{8}{4}=2$