Assignment #71. Here are some funcs that define random variables and their expectation.   Your job is to write ISETL funcs to add and multiply random variables.   Then prove that                   Exp( X .Plus Y) = Exp(X) + Exp(Y)   Explain how this is related to the way we began this course.   Find some conditions that make                   Exp( X .Times Y ) = Exp(X) * Exp(Y).        IsRanVar := func(X,space);        $ requires: you fill this in        $ effects : returns true if X is a random variable on space and        $           false otherwise            return is_set(space)            and forall x in space| is_number(X(x));        end;        MakeExpOp := func(pr opt space);        $ requires: pr is a density        $ effects : returns the expectation operator of pr        local Exp;            if space = OM then                space := domain(pr);            end;            Exp := func(X);            $ requires: X is a random variable on space                return %+[ X(s)*pr(s): s in space];            end;            return Exp;        end;2. Write the funcs indicated below. Check the correctness of your answerswith the use of the Num____ funcs of Assignment #5 and/or any other method.Try to make your code direct and efficient. Do not use the RandTup,..,etcfuncs; we will discuss why not in class.AllTups := func(k,S);$ requires: k is a positive integer; S is a set$ effects : returns the set of tuples with k elements from SAllSets := func(k,S);$ requires: k is a positive integer; S is a set$ effects : returns the set of sets with k elements from SAllPerms := func(k,S);$ requires: k is a positive integer; S is a set$ effects : returns the set of perms with k elements from SAllBags := func(k,S);$ requires: k is a positive integer; S is a set$ effects : returns the set of bags with k elements from S