The following interactions between binary and continuous variables are possible, with the exception of a. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$.
b. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$.
c. $Y _ { i } = \left( \beta _ { 0 } + D _ { i } \right) + \beta _ { 1 } X _ { i } + u _ { i }$.
d. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + u _ { i }$.

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The Answer of The following interactions between binary and continuous variables are possible, with the exception of a. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$.
b. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$.
c. $Y _ { i } = \left( \beta _ { 0 } + D _ { i } \right) + \beta _ { 1 } X _ { i } + u _ { i }$.
d. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + u _ { i }$.