# Thread: Question on exponential distributions

1. ## Question on exponential distributions

from an exponential distribution with expected value 0.2, if i get the mean of 20 observations, then repeat (get another 20) , etc, so in total 1000 times so 1000 means, then compare it with doing the whole thing again but now with 100 observations, i notice that there are more mean values from the 100 observations experiment, that are closer to 0.2, what property of convergence in probability is this?

Is is strong law of large numbers or weak law of large numbers or something else?
And can someone explain briefly what the difference is between strong law and weak law, I read wiki, but that makes no sense to me.

Thanks

2. Essentially it's a consequence of a law of large numbers. As n gets larger, the probability of being close to the mean is going to 1. If you aren't interested in mathematical statistics or probability theory you probably don't need to be too concerned with the difference between the strong and weak laws. To the layperson the difference is rather technical (weak convergence is quite intuitive while strong convergence requires a more sophisticated view of random variables).