Just as $E(t)$ is defined as a probability density function $($p$.$d$.$f$.)$ in $t,$ normalized RTD function $E()$ is defined in terms of normalized time $=\frac{t}{}.$ Like $E(t),E()$ must also satisfy all properties of a p$.$d$.$f$.($namely$,$ being always positive, and the area under the curve being unity$).$ The only difference is in the transformation of the time coordinate, in that $t$ is replaced by $.$

a$.$ Show that $E()=E(t)$

b$.$ Show that zeroth moment of $E()$ is unity.

c$.$ Show that first moment of $E()$ is also unity.

d$.$ Develop expression for second moment of $E()$ in terms of second moment of $E(t)$ and $.$

e$.$ Develop expression for second central moment of in terms of second central moment of $E(t)$ and $.$

f$.$ What is zeroth moment of the normalized washout function $W()$ equal to$?$