Q2. What is the reason why the theorem 3 is incomplete?
As a solution to their uniqueness problem, Theorem 3 is incomplete, because it leaves open the question of whether two models FF and Fn can be equivalent for complete experiments with a finite number of objects when F and G are distributions of different types.
Q3. What is the result of a complete choice experiment with tl objects?
The result of a complete choice experiment with tl objects is a set of the formcontaining 2” - (n + 1) discrete probability distributions; one for each subset of two or more objects.
Q4. is the distribution of the sum of n i.i.d. random variables?
(Recall that a distribution is infinitely divisible if, for every n, it is the distribution of the sum of n i.i.d. random variables.
Q5. how would he have discovered the choice axiom?
113Now if Thurstone had, for some reason, decided on the double exponential distribution instead of the normal, he would in effect have discovered the Choice Axiom.
Q6. What is the definition of a system of choice probabilities?
A set of this form will be called a complete system of choice probabilities for n objects, and be denoted by (p,/C,}.Convention: Choice probabilities can nmer be zero OY one.
Q7. What is the case for a complete system of choice probabilities?
A complete system of choice probabilities {pJC,> satisfies the Case E’ model T(p, 02, r) iff there exist numbers (scale vahes) ur , u2 ,..., U, such that foreveryiandS,iESCC,,ps(i) = P[u, + Xi = Max{r+ + Xi 1 j E S}], (6)where X, , X, ,..., X, are normally distributed random variables with common mean CL, common variance u2, and Cov(X, , Xj) = ruz for all i and j, i # j.