Objective types Questions $-$ Answers $(1$ Marks each$)$

What $is$ the first order density function?

$a.\frac{d{f}_x(x_1\text{;}{t}_1)}{d{x}_1}$

$b.\frac{de{l}^2{f}_x(x_1,x_2\text{;}{t}_1,t_2)}{del{x}_{1}del{x}_2}$

$c.\frac{de{l}^N{f}_x(x_1,x_2,dots{x}_N\text{;}{t}_1,t_2,\text{d}\text{o}\text{t}\text{s}\text{,}{t}_N)}{del{x}_{1}del{x}_{2}dotsdel{x}_N}$

$d.$ None $of$ these.

What $is$ the second order density function?

$a.\frac{d{f}_x(x_1\text{;}{t}_1)}{d{x}_1}$

$b.\frac{de{l}^2{f}_x(x_1,x_2\text{;}{t}_1,t_2)}{del{x}_{1}del{x}_2}$

$c.\frac{de{l}^N{f}_x(x_1,x_2,dots{x}_N\text{;}{t}_1,t_2,\text{d}\text{o}\text{t}\text{s}\text{,}{t}_N)}{del{x}_{1}del{x}_{2}dotsdel{x}_N}$

$d.$ None $of$ these.

What $is$ the $N^{th}$ order density function?

$a.\frac{d{f}_x(x_1\text{;}{t}_1)}{d{x}_1}$

$b.\frac{de{l}^2{f}_x(x_1,x_2\text{;}{t}_1,t_2)}{del{x}_{1}del{x}_2}$

$c.\frac{de{l}^N{f}_x(x_1,x_2,dots{x}_N\text{;}{t}_1,t_2,\text{d}\text{o}\text{t}\text{s}\text{,}{t}_N)}{del{x}_{1}del{x}_{2}dotsdel{x}_N}$

$d.$ None $of$ these.

The mean value $of$ a random process $x(t)is$ equal $to$ the $m$

$a.{\displaystyle \underset{-}{\overset{}{}}}{f}_x(x,t)dx$

$b.{\displaystyle \underset{-}{\overset{}{}}}{x}^2{f}_x(x,t)dx$

$c.{\displaystyle \underset{-}{\overset{}{}}}x{f}_x(x,t)dx$

$d.$ None $of$ the above.

The cross$-$correlation formula $is$

$a.R(x,y$;$t_1,t_2)={\displaystyle \underset{-}{\overset{}{}}}{\displaystyle \underset{-}{\overset{}{}}}xy{f}_{xy}(x,y$;$t_1,t_2)dxdy$

$b.R(x,y$;$t_1,t_2)={\displaystyle \underset{-}{\overset{}{}}}{\displaystyle \underset{-}{\overset{}{}}}{x}^2{y}^2{f}_{xy}(x,y$;$t_1,t_2)dxdy$

$c.R(x,y$;$t_1,t_2)={\displaystyle \underset{-}{\overset{}{}}}{\displaystyle \underset{-}{\overset{}{}}}{f}_{xy}(x,y$;$t_1,t_2)dxdy$

$d.$ None $of$ the above.