Algorithm 1 int linearSearch(int A[0...n1], int val)

i = 0;

while i < n do

if val == A[i] then

return i;

end if

i + +;

end while

return 1;

Suppose before we call linearSearch we randomly permute (i.e., reorder) the elements in A. In the following problem, we will nd the expected asymptotic runtime of linearSearch.

a) (1 point) What is the best case asymptotic runtime of linearSearch on an array of n elements? What index must val be located at to elicit this runtime?

b) (1 point) What is the worst case asymptotic runtime of linearSearch on an array of n elements? What index must val be located at to elicit this runtime?

c) (1 point) For the sake of simplicity, assume val is in A. Let Xj be the random variable which, given an permutation of the elements in our array, is 1 if index A[j] will be checked in our linearSearch for that permutation and 0 otherwise. What is the expected value of Xj?

d) (1 point) Let X be the random variable which, given an permutation of the elements in our array, is the number of elements of A which will be checked in our linearSearch for that permutation. Dene X using n copies of the random variable dened in the previous step.

I need help please.