Discrete random variables (1 Viewer)

leehuan

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Trying to calculate the variance of the uniform distribution and I don't know what the trick is to simplify the horrible looking sum





edit: wait I just realised I forgot something elementary...
 
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leehuan

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Question out of interest

Just like how you can call the Poisson distribution a limit of the binomial distribution, would you be able to say that the geometric distribution is just the binomial distribution for n=1
 

InteGrand

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Question out of interest

Just like how you can call the Poisson distribution a limit of the binomial distribution, would you be able to say that the geometric distribution is just the binomial distribution for n=1
The Bernoulli distribution is the binomial distribution with n = 1. In fact, a Bin(n,p) random variable is just a sum of n i.i.d. (independent and identically distributed) Bern(p) (Bernoulli with parameter p) random variables.

The geometric distribution can be considered a special case of the negative binomial distribution with r = 1 (or r = something else, depending on what convention is used).

Negative binomial distribution: https://en.wikipedia.org/wiki/Negative_binomial_distribution.
 
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leehuan

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Ahh right
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EDIT Wow I am an idiot.. a "proportion"... (their final answer wanted alpha*n in the place of alpha basically)




(Ignore the alpha^2 bit for now)

 
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InteGrand

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Ahh right
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I'm doing something wrong.




(Ignore the alpha^2 bit for now)

What you are calculating is the probability that X ≤ alpha, but we need the probability that the proportion is less than or equal to alpha (whereas X is the number).

 

leehuan

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Hey, whatever happened to the statistics marathon thing?
 

leehuan

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Basically the classic HSC greatest coefficient but I've forgotten how to do simple arithmetic tonight.

 

leehuan

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Never made a thread for approximations so I'll throw this question in this thread...

 

leehuan

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I don't believe it matters whether you have a discrete or continuous random variable so I'm randomly chucking it in this thread, but can I please have a proper example on what statistical independence is?

Like I get that Pr(A∩B) = Pr(A)Pr(B) for statistical independence but I kinda roted it, and don't fully understand it.

Which is why whilst I somewhat get this, I don't fully get it:




Also can I have a brief refresher on why expectation is linear again? Can I just argue that because summation/integration is linear?
 

InteGrand

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I don't believe it matters whether you have a discrete or continuous random variable so I'm randomly chucking it in this thread, but can I please have a proper example on what statistical independence is?

Like I get that Pr(A∩B) = Pr(A)Pr(B) for statistical independence but I kinda roted it, and don't fully understand it.

Which is why whilst I somewhat get this, I don't fully get it:




Also can I have a brief refresher on why expectation is linear again? Can I just argue that because summation/integration is linear?




https://proofwiki.org/wiki/Condition_for_Independence_from_Product_of_Expectations
.



https://proofwiki.org/wiki/Linearity_of_Expectation_Function
.



http://math.stackexchange.com/quest...r-under-what-conditions-is-median-also-a-line .
 
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leehuan

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Is there some way that conditional probability is supposed to work with random variables?







And then I got lost.



Possibly useful: My textbook (Pg 3 & Pg 14) had an example where instead they used expectation. But they actually started counting at age 0, and I have to start counting at age 10 so I wasn't sure how to use expectation here.
 
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InteGrand

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Is there some way that conditional probability is supposed to work with random variables?







And then I got lost.



Possibly useful: My textbook (Pg 3 & Pg 14) had an example where instead they used expectation. But they actually started counting at age 0, and I have to start counting at age 10 so I wasn't sure how to use expectation here.
I think you would need to make an assumption about what the oldest possible age is, e.g. 100 years (or call it N years or something), because that'd clearly affect the answer.

Also, Pr(X > 10 | X = 10) is 0, so I think you meant something else.
 

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