$6.(10$ points$).$ The scalar product of two lists of integers xs and ys of length n is given by the sum of the products of their corresponding integers:

n$1$

$($xsi $$ ysi$)$ i$=0$

In a similar manner to chisqr $($defined below$),$ show how a list comprehension can be used to define a function scalarproduct :: $[$Int$]->[$Int$]->$ Int that returns the scalar product of two lists. For example $($in GHCi$)$:

$>$ scalarproduct $[1,2,3][4,5,6]$

$32$

Note: that the mathematical equation for computing the chi$-$square statistic for comparing lists os and es of length n is given by the following sum:

and can be represented in Haskell as:

chisqr :: $[$Float$]->[$Float$]->$ Float

chisqr os es $=$ sum $[(($o$-$e$)^2)/$e $|($o$,$e$)<-$ zip os es$]$

n$1($osi $$ esi$)2$

esi

$$

i$=0$

$2$

Hint: Since the scalar product of a pair of lists is also $$zipping$$ a pair of lists $($but doing something slightly different with the pairs$),$ it will be defined quite similarly, i$.$e$.,$ with a list comprehension involving zip.