The distributed lag model is given by a. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } Y _ { t - 1 } + u _ { t }$.
b. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + \beta _ { 2 } Y _ { t - 2 } + \ldots + \beta _ { r } Y _ { t - r } + u _ { t }$.
c. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } u _ { t } + \beta _ { 2 } u _ { t + 1 } + \beta _ { 3 } u _ { t + 2 } + \ldots + \beta _ { r + 1 } u _ { t + r } + e _ { t }$.
d. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } X _ { t - 1 } + \beta _ { 3 } X _ { t - 2 } + \ldots + \beta _ { r + 1 } X _ { t - r } + u _ { t }$.

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The Answer of The distributed lag model is given by a. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } Y _ { t - 1 } + u _ { t }$.
b. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + \beta _ { 2 } Y _ { t - 2 } + \ldots + \beta _ { r } Y _ { t - r } + u _ { t }$.
c. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } u _ { t } + \beta _ { 2 } u _ { t + 1 } + \beta _ { 3 } u _ { t + 2 } + \ldots + \beta _ { r + 1 } u _ { t + r } + e _ { t }$.
d. $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } X _ { t - 1 } + \beta _ { 3 } X _ { t - 2 } + \ldots + \beta _ { r + 1 } X _ { t - r } + u _ { t }$.

The Distributed Lag Model Is Given by A Yt=β0+β1Xt+β2Yt−1+utY _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } Y _ { t - 1 } + u _ { t }Yt​=β0​+β1​Xt​+β2​Yt−1​+ut​

The Distributed Lag Model Is Given by A $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } Y _ { t - 1 } + u _ { t }$