Consider two mutually independent random variables ${v_1},{v_2}$, which are the Gaussian white noise with distribution $N(0,1)$. We suppose they satisfy the following equation $({v_1}+a_1){w_1} + ({v_2}+a_2){w_2} = 0$, where ${a_1},{a_2}$ are the given constants, ${w_1},{w_2}$ are some values to be determined. My question is whether $a_1{w_1} +a_2{w_2}$ has the zero expectation? Can anyone help me?
2026-04-02 03:12:22.1775099542
An equation about random variables
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