Two mutually exclusive and feasible events are always dependent. Two independent and feasible events cannot be mutually exclusive. What is wrong here?
In stratified sampling, the strata are mutually exclusive. The independence of the samples from two different strata is consequence of the independent sampling design in each stratum.
Moreover, in stratified sampling, all the strata are sampled with probability 1. Then, the probability of sampling two different strata is 1. And consequently the event A1 "an stratum is sampled", and the event A2 "other stratum is sampled", are independent because p(A1A2) = 1 = 1·1 = p(A1)p(A2).
In each event of stratified sampling both strata are sampled (both strata are dependent because they occur simultanuously in any stratified sampling).
Two Strata are Mutually Exclusive, and Not mutually independent...The Two random samples from these two strata are Mutually Independent indeed..........
In stratified sampling, the strata are mutually exclusive. The independence of the samples from two different strata is consequence of the independent sampling design in each stratum.
Moreover, in stratified sampling, all the strata are sampled with probability 1. Then, the probability of sampling two different strata is 1. And consequently the event A1 "an stratum is sampled", and the event A2 "other stratum is sampled", are independent because p(A1A2) = 1 = 1·1 = p(A1)p(A2).
In each event of stratified sampling both strata are sampled (both strata are dependent because they occur simultanuously in any stratified sampling).
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