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> Urgent Maths/Probability Question, confirmation of theory please?

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TSLightningFist
post Oct 1 2013, 01:01 PM, updated 7y ago

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If X1, X2, X3, ... , Xn are independent and identically distributed random variables,

Is the conditional distribution f(X1 + X2 + X3 + ... + Xn | X1) = X1 + f(X2 + X3 + ... + Xn) ?

Thanks!
mumeichan
post Oct 1 2013, 06:00 PM

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What does the + sign mean? Union? And what is the f for?

In any case

P(A ∩ B|A)=P(A)xP(B)/P(A)=P(B)

This post has been edited by mumeichan: Oct 1 2013, 06:08 PM
RyukA
post Oct 2 2013, 12:35 AM

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QUOTE(LightningFist @ Oct 1 2013, 01:01 PM)
If X1, X2, X3, ... , Xn are independent and identically distributed random variables,

Is the conditional distribution f(X1 + X2 + X3 + ... + Xn | X1) = X1 + f(X2 + X3 + ... + Xn) ?

Thanks!
*
hahaha. Boris's assignment.

hint: apply convolution to get the marginal distribution of X1.

since X1 and Sn = X1+...+Xn, is not independent.




TSLightningFist
post Oct 2 2013, 06:06 AM

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QUOTE(RyukA @ Oct 2 2013, 12:35 AM)
hahaha. Boris's assignment.

hint: apply convolution to get the marginal distribution of X1.

since X1 and Sn = X1+...+Xn,  is not independent.
*
Jacobian change of variable. Hahaha. Reverse convolution.

But the da an very lansi one

 

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