Let X, and S = E(X; – Xn)²/(n – 1) be the sample mean and variance, respectively, of iid random variables X1,..., Xn. Then suppose another iid random variable, Xn+1, becomes available. Show that a) Xn+1 nX + Xn+1 %3D n +1 ns2 Pn+1 n b) = (n – 1)S, + n +1 %3D z("X – I+ux)-

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Let X, and S = E1(X; – Xn)²/(n – 1) be the sample mean and variance, respectively, of iid
random variables X1,..., Xn. Then suppose another iid random variable, Xn+1, becomes available.
Show that
nX + Xn+1
a)
Xn+1
n +1
n
ns1 = (n – 1)S +
-(Xn+1 - Xn)².
n +1
b)
n+1
Transcribed Image Text:Let X, and S = E1(X; – Xn)²/(n – 1) be the sample mean and variance, respectively, of iid random variables X1,..., Xn. Then suppose another iid random variable, Xn+1, becomes available. Show that nX + Xn+1 a) Xn+1 n +1 n ns1 = (n – 1)S + -(Xn+1 - Xn)². n +1 b) n+1
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