This homework assignment is about expected values and chained hash tables. Procedures are written in Cormen$$s pseudocode. Make sure you know how Cormen$$s pseudocode works before you begin: it may work differently from what you expect.

$1.(10$ points.$)$ Let$$A$$be an array of$$n$$integers$,$ where$$n$>0.$ The procedure ARRAY$-$SEARCH$$searches$$A$$for an integer element$$e$.$If it finds$$e$,$then it returns$$TRUE$,$ otherwise it returns$$FALSE$.$

ARRAY$-$SEARCH$($A$,$e$,$n$)$

$01$for$$k$=1$to$$n

$02$if$$A$[$k$]==$e

$03$return$$TRUE

$04$return$$FALSE

Suppose that the test in line $02$ succeeds with probability $1/$n$.$What is the expected value of the total number of comparisons made by line $02?$ Your answer must not use$$O$,,$ or $$ notation. Prove that your answer is correct