Let  $A=\{1,2,3,4\}$  and S be the set of all mapping from A to A. One mapping f is selected at random from S. Let X be the number of elements of ‘A’ which are having self images with respect to f then the value of   $E\left(X\right)=$

$\begin{array}{l}X=x: 0 1 2 3 4\\ p(X=x): \frac{D_4}{4!}\left|\frac{{ }^4{C}_1\times D_3}{4!}\right|\left|\frac{{ }^4{C}_2\times D_2}{4!}\right|\text{\hspace{0.17em}}\left|0\right|\left|\frac{1}{4!}\right|\end{array}$

Where $D_k$  is de-arrangement of k things
 $$\begin{gathered} E\left(X\right)=\sum [x.p(X=x)] \\ \Rightarrow E\left(X\right)=1 \end{gathered}$$