The textbook formula for the variance of the discrete random variable Y is given as $\sigma _ { Y } ^ { 2 } = \sum _ { i = 1 } ^ { k } \left( y _ { i } - \mu _ { Y } \right) ^ { 2 } p _ { i }$ Another commonly used formulation is $\sigma _ { y } ^ { 2 } = \sum _ { i = 1 } ^ { k } y _ { i } ^ { 2 } p _ { i } - \mu _ { y } ^ { 2 }$ Prove that the two formulas are the same.

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The Answer of The textbook formula for the variance of the discrete random variable Y is given as $\sigma _ { Y } ^ { 2 } = \sum _ { i = 1 } ^ { k } \left( y _ { i } - \mu _ { Y } \right) ^ { 2 } p _ { i }$ Another commonly used formulation is $\sigma _ { y } ^ { 2 } = \sum _ { i = 1 } ^ { k } y _ { i } ^ { 2 } p _ { i } - \mu _ { y } ^ { 2 }$ Prove that the two formulas are the same.

The Textbook Formula for the Variance of the Discrete Random σY2=∑i=1k(yi−μY)2pi\sigma _ { Y } ^ { 2 } = \sum _ { i = 1 } ^ { k } \left( y _ { i } - \mu _ { Y } \right) ^ { 2 } p _ { i }σY2​=∑i=1k​(yi​−μY​)2pi​

The Textbook Formula for the Variance of the Discrete Random $\sigma _ { Y } ^ { 2 } = \sum _ { i = 1 } ^ { k } \left( y _ { i } - \mu _ { Y } \right) ^ { 2 } p _ { i }$