Basic stats Question
- Thread starter praveenraj
- Start date
Looks fine to me.
\[ \sigma^2(X)=E(X^2)-E(X)^2 \]
\[ \therefore \sigma(X)=\sqrt{E(X^2)-E(X)^2} \]
If your spreadsheet is set up correctly you should just be able to change the probabilities to get back to the example 50/50 numbers. You could also memorise the common quantities for a bernoulli. i.e. \( \mu=p \) and \( \sigma^2=pq \) where \(p=P(X=1)\) and \(q=1-p=P(X=0)\)
\[ \sigma^2(X)=E(X^2)-E(X)^2 \]
\[ \therefore \sigma(X)=\sqrt{E(X^2)-E(X)^2} \]
If your spreadsheet is set up correctly you should just be able to change the probabilities to get back to the example 50/50 numbers. You could also memorise the common quantities for a bernoulli. i.e. \( \mu=p \) and \( \sigma^2=pq \) where \(p=P(X=1)\) and \(q=1-p=P(X=0)\)
HI @praveenraj Here is XLS with "unfair" coin that has probabilities 70/30%: https://www.dropbox.com/s/568wedbnq79rsy6/121719-unfair-coin-variance.xlsx?dl=0
The simple test is σ^2(Bernoulli) = p*(1-p), in this case, 70%*30% = 0.210.
The simple test is σ^2(Bernoulli) = p*(1-p), in this case, 70%*30% = 0.210.
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