# Which is correct between the number of and the numbers of?

I am making presentation material about mathematical.

The numbers of events occurred in each sub-interval are independent.

or

The number of events occurred in each sub-interval are independent.

Which is correct? Thank you for reading my question. :)

X = the number of event occurred in 0s ~ 10s.

Y = the number of event occurred in 10s ~ 13s.

Z = the number of event occurred in 13s ~ 20s.

I want to say "X, Y and Z are stochastically independent".

How can I write the sentence above?

• Neither. Wait, it's gets worse. I don't even know what you're asking. How is anything mathematical? Have the events occurred already? Who or what is independent? Don't take this personally, but you might be better off at ELL. Jan 12, 2016 at 8:26
• People, stop downvoting stuff anonymously, it's uncouth. Jan 12, 2016 at 8:27
• @Ricky Thank you for your interest. I edited my question. Jan 12, 2016 at 8:38

Since you refer to each (singular) sub-interval, number should also be singular. Assuming that an independent number makes sense in your field of study, you could say:

The number of events occurring in each sub-interval is independent.

If the word independent requires two arguments (X is independent of Y), you could say:

In each sub-interval, the number of events occurring is independent of that of any other sub-interval.

It may be better to use multiple but simpler sentences to express your final sample sentence:

Let X_i be the number of events occuring in sub-interval i. Then the X_i are stochastically independent.

• I'm impressed with your good answer. I chose second one. Thank you very much. Jan 12, 2016 at 9:31