for unequal probability sampling with replacement i have an auxiliary variable that the probability of selecting an element should be proportional to but i dont know how to find what the probability would be.
element# value auxilary variable
1 12 5
2 18 3
3 25 1
how do i find what the probability of selecting say sample 1,2.
i thought it would be (5/9)*(3/9) but when add up all possible samples the probabilities dont add to one so it doesnt make sense.