The transfer function H$($z$)$ of a discrete time system is given below

H$($z$)=(2-(3)/(4)$z$^(-1))/(1-(3)/(4)$z$^(-1)+(1)/(8)$z$^(-2))$

Consider the statements given below:

Statement $1$: The system is causal and stable for $|$z$|>(1)/(2)$

Statement $2$: The system is stable but not causal for $|$z$|<mi>(</mi><mn>1</mn><mi>)</mi><mi>/</mi><mi>(</mi><mn>4</mn><mi>)</mi>$

Statement $3$: The system is neither causal nor stable for $(1)/(4)<mi>|</mi>$z$|<mi>(</mi><mn>1</mn><mi>)</mi><mi>/</mi><mi>(</mi><mn>2</mn><mi>)</mi>$

Identify the correct statement$($s$)$

Statement $1$ alone is true

Statement $2$ alone is true

Statement $3$ alone is true

Statements $1$ and $2$ are true

Statements $1$ and $3$ are true

Statements $2$ and $3$ are true

All three statements are true

Consider a discrete time signal x$[$n$]$ defined below

x$[$n$]=($n$+1)^(2)$u$[$n$]$

Determine the Z transform and the corresponding ROC. The value the Z transform at z$=2,$ that

is x$(2)$ is

Find the Z transform, x$($z$)$ of the discrete time signal x$[$n$]$

x$[$n$]=5((1)/(4))^(|$n$|)$

Let the corresponding ROC be x$(1\mathrm{.}5)$r$\_(1)<mi>|</mi>$z$|$

The value of x$(1\mathrm{.}5)$ will be