A simple probability theory question, but the answer may not be simple.

#1
Hi, I have the following question.

Suppose I draw a measure of 0<m<1 points uniformly without replacement from [0,1]. What is the probability that less than or equal to a measure of 0<k<m<1 points are drawn from the interval [i,1]? WLOG, suppose k<1-i.

An example: a measure of 1/3 points are drawn uniformly without replacement from [0,1]. What is the probability that less than or equal to a measure of 1/4 points are drawn from [1/2,1]?

I think the probability that an exact measure of 1/4 points are drawn from [1/2,1] is 0, so I am asking the CDF in the question. Hope I am correct.

Thank you very much.
 
#2
Clarify the first sentence:

I mean draw the points randomly from the interval [0, 1], with each remaining point being drawn with equal probability.

Thanks.
 

BGM

TS Contributor
#3
Not sure about your question.

The very first concept to clarify is that if you are sampling from a continuous distribution, then it is almost surely that you will not sample the same point again (i.e. with probability 1). So you do not need to mention "without replacement" in this case. "Without replacement" is used only when the population size is finite.