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Could any one anyone help me figure out the the probability density function of |X|^(1/2)+|Y|^(1/2)+|Z|^(1/2) if X, Y and Z are distributed normally with mean 0 and variance 1, N(0,1) ?

Thanks in advance.

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A probability density function question

Could any one help me figure out the the probability density function of |X|^(1/2)+|Y|^(1/2)+|Z|^(1/2) if X, Y and Z are distributed normally with mean 0 and variance 1, N(0,1) ?

Thanks in advance.