Probability question (math nerds welcome)

[MadMojoMonkey]

None of this sits well with me. That tiny range after 100 trials is too low. This says that you expect to have exactly $0 after 100 trials about 19 times out of every 20 experiments. Gut check says no.

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Isn't StDev = sqrt(2) units per trial? So StDev after 100 trials is 141.4?

141.4 /sqrt(100) = 14.14
14.14*1.92 = 27.15

Using 1.96 is for "infinite trials", and generally is a fine approx for more than 20 trials, but since 1.92 is technically correct here, I'm using it.

(I start work in 15 minutes, so I can't really get into this right now. I'll think on it this afternoon.)

[jackvance]

None of this sits well with me. That tiny range after 100 trials is too low. This says that you expect to have exactly $0 after 100 trials about 19 times out of every 20 experiments. Gut check says no.

Confidence interval is about the mean of the sample. So if you have +19 after 100 samples, the mean of 0.19 is still in the confidence interval.

Isn't StDev = sqrt(2) units per trial? So StDev after 100 trials is 141.4?

lol no

[MadMojoMonkey]

Gut check says no.

We're talking about the expected outcome after 100 trials, not the expected outcome of each of the trials.

[jackvance]

Gut check says no.

We're talking about the expected outcome after 100 trials, not the expected outcome of each of the trials.

We actually seem to come to the same conclusion, with only the 1.92 and 1.96 difference.

14.14*1.92 = 27.15

So your interval [-27.15, +27.15]

This is not the confidence interval though because is strictly about the mean. Probably this has a name in statistics though.

But please look it up.

[MadMojoMonkey]

Gut check says no.

We're talking about the expected outcome after 100 trials, not the expected outcome of each of the trials.

We actually seem to come to the same conclusion, with only the 1.92 and 1.96 difference.


So your interval [-27.15, +27.15]

This is not the confidence interval though because is strictly about the mean. Probably this has a name in statistics though.

But please look it up.

Sorry. The posts were coming fast and I was behind the thread, and I tried to delete this response before I started my shift, but I guess it missed.

I agree with this range.

EDIT: The CI should be symmetric about the mean. We're using a normal distribution, which is symmetrical about the mean, to model the outcome.

[Renton]

Isn't StDev = sqrt(2) units per trial? So StDev after 100 trials is 141.4?

Variance is additive, standard deviation is not. St.Dev for 100 trials is 14.14 units / 100 trials. I am fairly certain of that much.