Haskell The "scalar product" of two lists of integers "xs" and "ys" of length "n" is given by the sum of the products of corresponding integers in slide 21 for chapter 5. In a similar manner to "chisqr" (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] 14,5,6] 32 Note that the mathematical equation for computing the "chi-square statistic" at the beginning of subsection "Cracking the cipher" in section 5.5 of the Haskell textbook

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Haskell The "scalar product" of two lists of integers "xs" and "ys" of length "n" is given by the sum of the products of corresponding integers in slide 21 for chapter 5. In a similar manner to "chisqr" (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] 14,5,6] 32 Note that the mathematical equation for computing the "chi-square statistic" at the beginning of subsection "Cracking the cipher" in section 5.5 of the Haskell textbook is literally "zipping" a pair of lists "oe" and "es", and can hence be represented in Haskell as: chisqr :: [Float] -> [Float] -> Float chisqr os es = sum ((o-e) ^2)/e | (o,e)
(3) The scalar product of two lists of integers xs
and ys of length n is give by the sum of the
products of the corresponding integers:
n-1
Σ(xs₁ * ys₁ )
i=0
Using a list comprehension, define a function
that returns the scalar product of two lists.
21
Transcribed Image Text:(3) The scalar product of two lists of integers xs and ys of length n is give by the sum of the products of the corresponding integers: n-1 Σ(xs₁ * ys₁ ) i=0 Using a list comprehension, define a function that returns the scalar product of two lists. 21
(2) A positive integer is perfect if it equals the sum
of all of its factors, excluding the number itself.
Using a list comprehension, define a function
perfects :: Int → [Int]
that returns the list of all perfect numbers up
to a given limit. For example:
> perfects 500
[6,28,496]
20
Transcribed Image Text:(2) A positive integer is perfect if it equals the sum of all of its factors, excluding the number itself. Using a list comprehension, define a function perfects :: Int → [Int] that returns the list of all perfect numbers up to a given limit. For example: > perfects 500 [6,28,496] 20
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