GR0177 question 16

[polaritons]

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.

[bfollinprm]

Experimental errors are reset in the 10 1 second experiments. While the statistical error is the same, the systematic error will be significantly less in 10 1 second trials.

[vikrambijarniya]

technically both things are same. but practically it depends on the situation. say you have to calculate time period of simple pendulum. then a 10 seconds experiment can give u more accurate result then 10 1 second experiments.