Consider three observations \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) such that
\( \mathrm{P}^{127} \) \( \mathrm{b}=\mathrm{a}+\mathrm{c} \). If the standard deviation of \( \mathrm{a}+2, \mathrm{~b}+2 \),
W \( \mathrm{c}+2 \) is \( \mathrm{d} \), then which of the following is true?
(1) \( \mathrm{b}^{2}=3\left(\mathrm{a}^{2}+\mathrm{c}^{2}\right)+9 \mathrm{~d}^{2} \)
(2) \( b^{2}=3\left(a^{2}+c^{2}\right)-9 d^{2} \)
(3) \( \mathrm{b}^{2}=3\left(\mathrm{a}^{2}+\mathrm{c}^{2}+\mathrm{d}^{2}\right) \)
(4) \( b^{2}=a^{2}+c^{2}+3 d^{2} \)
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