standard deviation. coins

Forums: Probability
Email this Topic • Print this Page

I am trying to understand a situation.

Suppose you recieved a coin toss 3000-trial-sample.

Tails hit +3 standard deviations.

We start a new test, this time 1000 tosses. Tails hit +1.5 standard deviations.
We make another 1000-test with +1.5sd again to tails.

Questions:

1)what is the chance for this event( 2 1000-test with +1.5sd on the same side) to be random?
2)what if we make 1 2 or more 1000-tests with the same result? We do we get the 99% confidence of the unfairness of the coin ?
3)might we take the first 3000-test as a prior probability and use Bayes rules?

I apologize if I confused some conceps

Warm regards
Ybot

Topic Stats
Top Replies
Link to this Topic

Type: Discussion • Score: 1 • Views: 894 • Replies: 10

No top replies

@ybot,

1) The standard deviation is sqrt(0.5x0.5x1000)=15.8 so the results for the first two trials were tails = 500 + 1.5x15.8 = 524. Now consider the two trials together. 1048 out of 2000. The standard deviation for 2000 flips is 22.4 meaning that you are now at 2.15 standard deviations. You can get that probability from a z score table.

2) Repeat the same exercise with a third trial and you should be past 99%.

1 Reply

@engineer,

Yes, 524 is +1.5sd for 1000.
At 2000 we have got 1048=+2.15sd ok.
It happens in 1 in 15 random 2000 samples.
In case we have another 524/1000 we have got 1572/3000, means +2.75 sd.
Can we determine this coin is unfair with these 3000 trials?, +2.75 sd is not too much.
And, how could we use the previous 3000 trials?(the ones before the 2nd 3000)

1 Reply

@ybot,

Sorry,the chance for +2.15 standard deviation is not 1/15, its more close to 1./25

0 Replies

@ybot,

Simply; the more tosses, the closer it comes out 50/50.

The +/- 1.5 in 1000 toss is only 15.

1 Reply

@cicerone imposter,

1000 tosses, 1.5sd=24
2000 tosses, 1.5sd=33.5
3000 tosses 1.5sd=41.1

But, when we could be confident of the unfairness of this coin?

1 Reply

@ybot,

Thanks, ybot, for that correction.

1 Reply

@cicerone imposter,

So, any idea of the time we might be comfortable saying "this coin is unfair"?

1 Reply

@ybot,

Yea, when you lose a high stakes bet.

1 Reply

@cicerone imposter,

You can lose or win at +/- 3.5 sd range.
Beyound this threshold you suspect.
I'd like to find a mathematical way to detect it.

1 Reply

@ybot,

I took statistics in college, but that was over 40 years ago. If you don't use it, you lose it.

0 Replies

standard deviation. coins

Related Topics

Quick Links

My Account

able2know