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On lottery there are $100$ losing tickets and $20$ winning tickets. We draw with return, until we draw winning ticket. How many times on average do we have to draw to get winning ticket?

What's the standard deviation?

So its obviously geometric distribution (Bernoulli)

Chance to draw winning ticket is $\frac{1}{6}$

I can put it into the formula but I don't know how to calculate the average.

What am I supposed to put as random variable $i$?

$P(X=i)=(1-\frac{1}{6})^{i-1}\frac{1}{6}$

Answer:

Formula for computing the expected value of a geometric distribution = $\frac{1}{p}$

$p=\frac{1}{6}$

$\frac{1}{\frac{1}{6}}=6$

6 times on average untill we draw winning ticket.

StubbornAtom
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fakeraker p
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  • Do you know a formula for computing the expected value of a geometric distribution? – N. F. Taussig Sep 04 '20 at 20:31
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    @N.F.Taussig I didn't know but I quickly googled it. Formula would be 1/p? Then the answer is $\frac{1}{\frac{1}{6}}=6$. Seems too simple. – fakeraker p Sep 04 '20 at 20:39
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    https://math.stackexchange.com/questions/1196452/expected-value-of-the-number-of-flips-until-the-first-head/1196478#1196478 for a proof. The result for the standard deviation should also be readily available on searching and proofs for that also scattered around this site. – JMoravitz Sep 04 '20 at 20:42
  • Its beyond me why its not included in my lecture pdf and yet it was on the test. This task is from my last exam that I didn't pass, If I have gotten it right I would pass with minimum required... Thanks for help guys. – fakeraker p Sep 04 '20 at 20:45

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