The textbook derived the following result: $\hat { \beta } _ { 1 } \stackrel { p } { \longrightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$ Show that this is the same as $\hat { \beta } _ { 1 } \stackrel { p} { \longrightarrow }\beta _ { 1 } \frac { \sigma _ { w } ^ { 2 } } { \sigma _ { w } ^ { 2 } + \sigma _ { X } ^ { 2 } } \beta _ { 1 }$

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The Answer of The textbook derived the following result: $\hat { \beta } _ { 1 } \stackrel { p } { \longrightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$ Show that this is the same as $\hat { \beta } _ { 1 } \stackrel { p} { \longrightarrow }\beta _ { 1 } \frac { \sigma _ { w } ^ { 2 } } { \sigma _ { w } ^ { 2 } + \sigma _ { X } ^ { 2 } } \beta _ { 1 }$

The Textbook Derived the Following Result Show That This Is the Same As