Show that X-bar is more efficient

Let population X be normal with mean μ and varianceσ2 .We select two samples X1 andX2 from the population.(a)Show θ-hat is unbiased if θ-hat =a1X1…

Let population X be normal with mean μ and varianceσ2 .We select two samples X1 andX2 from the population.(a)Show θ-hat is unbiased if θ-hat =a1X1 + a2X2 for alla1 , a2 >=0 witha1+a2 = 1.(b)Show that X-bar is more efficient that θ-hatfor all a1 , a2 >=0 witha1+ a2 = 1.Thanks for trying.
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