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Explore Stack InternalI do not know the actual expression for Var($y$), but to get started, $y$ will not follow a normal distribution and its cumulative probability distribution $F_Y(x)$ will be the product of the cumulative distributions $F_{X1}(x)$ and $F_{X2}(x)$, floored to zero for $x<C$.
For an estimation of Var($y$) you may find this other question helpful: Expectation of the maximum of gaussian random variablesExpectation of the maximum of gaussian random variables
I do not know the actual expression for Var($y$), but to get started, $y$ will not follow a normal distribution and its cumulative probability distribution $F_Y(x)$ will be the product of the cumulative distributions $F_{X1}(x)$ and $F_{X2}(x)$, floored to zero for $x<C$.
For an estimation of Var($y$) you may find this other question helpful: Expectation of the maximum of gaussian random variables
I do not know the actual expression for Var($y$), but to get started, $y$ will not follow a normal distribution and its cumulative probability distribution $F_Y(x)$ will be the product of the cumulative distributions $F_{X1}(x)$ and $F_{X2}(x)$, floored to zero for $x<C$.
For an estimation of Var($y$) you may find this other question helpful: Expectation of the maximum of gaussian random variables
I do not know the actual expression for Var($y$), but to get started, $y$ will not follow a normal distribution and its cumulative probability distribution $F_Y(x)$ will be the product of the cumulative distributions $F_{X1}(x)$ and $F_{X2}(x)$, floored to zero for $x<C$.
For an estimation of Var($y$) you may find this other question helpful: Expectation of the maximum of gaussian random variables
