Question

# Consider the problem from Lecture 4, “Search, Sampling and Independence.” Assume that the distribution of prices...

Consider the problem from Lecture 4, “Search, Sampling and Independence.” Assume that the distribution of prices from which the consumer draws is (i) continuous and (ii) Uniformly distributed on the interval [ ¯ p, ¯ p]. (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?
(c) Intuitively, why is your answer diﬀerent from the case of the discrete price distribution?

solution:

a)

The consumer is lost in the mall and doesn't remember the last store he visited and cannot avoid the possibility of returning to the same store (i.e. the last price he drew), successive price draws are independent

Since there is probability will not depend on each other in this particular case

b)

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

Since there is probability will depend on each other in this particular case

c) The answer is different from the case of the discrete price distribution because here the condition cannot/can avoid the possibility of returning to the same store is creating independence/dependence.

The prices are uniformly distributed

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