Question

Consider the problem from Lecture 4, “Search, Sampling and Independence.” Assume that the distribution of prices from which the consumer draws is (i) discrete and (ii) Uniformly distributed with N possible stores/prices from which to draw.
(a) If the consumer is lost in the mall and doesn’t remember the last store he visited (i.e. the last price he drew) and so cannot avoid the possibility of returning to the same store, are successive price draws dependent or independent?
(b) If the consumer is lost in the mall and does remember the last store he visited (i.e. the last price he drew) and so can avoid the possibility of returning to the same store, are successive price draws dependent or independent?

Answer 1

Answer:

(a) If the consumer is lost in the mall and doesn’t remember the last store he visited (i.e. the last price he drew) and so cannot avoid the possibility of returning to the same store, are successive price draws dependent or independent?

Answer:

Consumer is lost in the mall and he doesn't remember the last stage he visited.Therefore,  the successive draws will be dependent,since  flake is still probability that he can visit he same store, and this is the all other probability

On uniform distribution
p(X=x) =1/N

(b) If the consumer is lost in the mall and does remember the last store he visited (i.e. the last price he drew) and so can avoid the possibility of returning to the same store, are successive price draws dependent or independent?

Answer:

If he  does remember the last store he visited then he will avoid to visit at this store,success price draw will be independent of visiting the store.