Question: Let Y be a random variable with E[Y ] and 2 var[Y ]. Define g y,,2 y

Let Y be a random variable with ¹ Æ E[Y ] and ¾2 Æ var[Y ]. Define g

¡

y,¹,¾2¢

Æ

Ã

y ¡¹ ¡

y ¡¹

¢2

¡¾2

!

.

Let (b¹,b¾

2) be the values such that g n(b¹,b¾

2) Æ 0 where g n(m, s) Æ n¡1Pni

Æ1 g

¡

yi ,m, s

¢

. Show that b¹ andb¾

2 are the sample mean and variance.

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