X e Y, random independent variables with mean zero and equal variances. If $Z=X+Y,$ I need to find $E[Z^2|=]$ for any x value in the defined conditional distribution.
Is this correct?
$$E[(+)^2|=]=E[^2|=]+E[Y^2|=]+E[2XY|=]=$$ $$=x^2+E[Y^2|=]+2xE[Y]=x^2+E[Y^2]$$