Question

You have these 10 observations of some event X:
1.03
1.022
1.022
1.01
1.026
1.02
0.95
1.005
1.05
1.023

Here is the sorted list from least to greatest:
0.95
1.005
1.01
1.02
1.022
1.022
1.023
1.026
1.03
1.05

Based on this data alone:
1) It makes sense to say P(X <= 0.95) = 1/10 correct? We might say there is a 1/10 chance that X <= 0.95.
2) It makes sense to say P(X >= 1.01) = 8/10 correct? We might say there is an 8/10 chance that X >= 1.01.
3) My real question: What is the chance that we will see an observation of X >= 1.01 before we see an observation of X <= 0.95? Can this be calculated with this information?

My guess at an answer to #3:

Since P(X >= 1.01) = 8/10 is eight times P(X <= 0.95) = 1/10, can we say that overall the probability that we see X >= 1.01 before we see X <= 0.95 is 8/9? As in:
Event I: 8/9 chance that X >= 1.01 before X <= 0.95
Event II: 1/9 chance that X <= 0.95 before X >= 1.01
Total Probability: 8/9+1/9 = 1, which makes sense since Event I and Event II together are collectively exhaustive, and 8/9 is 8 times 1/9.

Is this correct for #3? If not, or even if so, is there some standard (“named”) statistical procedure/distribution that deals with answering the question posed in #3?

Thanks for your thoughts.

Answer 1

I began to think of the binomial distribution with the common heads or tails coin flipping experiment example...I believe my question in #3 is related to that, and in fact I think the generalization is what applies, the "multinomial" distribution...any thoughts from any learned stat tutors?

Answer 2

waste of waste