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signal detection in noise

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sib

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hi ,

i have a question . I have a vector of noise samples which i know are from a Gaussian distribution (say mean=0, var=1) and i have a vector of signal samples (IID RV with mean=0 and var=1, UNKNOWN PDF). Now my question is that when they are added up , what does the resulting pdf look like, is it a gaussian (mean=0, var=2) or something else.
 

The result will have a Gaussian pdf
 
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    sib

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Well, this is true only when the set of samples are relatively large.
 

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