Question: 4) For stratified sampling, the population variance in stratum h is Nn ( ynj - Yn) Sh = Nn - 1 j=1 a. Show that

4) For stratified sampling, the population variance in stratum h is Nn ( ynj - Yn) Sh = Nn - 1 j=1 a. Show that Sh = ~ 1 Nh - 1 b. Let bri be a random variable where 1, if j E Sn bnj = 10, otherwise' nn then Var (buj) = nn - nn and Cov( bnj, bnk ) = nn 1 Nh LNh(Nh-1) Nh-1] Nn Nn Show that Var (ystr) = En=1 Nn Sh . Hint: > >lazb Xaxb = Za=12b=1Xaxb -Za=1xa

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