I guess my question is more on statistics rather than the actual question.

My first question:

Is it equivalent to have 10 trials of 1 second interval experiment and 1 trial of 10 seconds interval experiment. Since supposedly in a Poisson experiment each interval of time is suppose to be independent of each other, then shouldn't the 10 trials of 1 second be equivalent to just 1 trial of 10 seconds?

My second question:

Isn't it weird to have the mean same as the variance? I mean what if I just have 1 trial? And that 1 trial yielded a count of 2. Then my standard deviation is square root of 2? Does this mean doing 10 1-second interval trials previously and doing 1 1-second interval trial give the same uncertainty?

This question has been bugging for way longer than it should. I hope someone can help me out with these questions.