Question

Given μ₁=0, μ₃=1, and 0≤ μ₂≤1, show that SUM(μ₁- μ.)² is minimized when μ₂=0.5 where μ. = (μ₁+ μ₂+ μ₃)/3

Answer 1

Another method can be that we have to minimize the variance*3 and variance is minimum for the symmetric data so variance will be minimum when ₁ and  2have the same difference as  2and  3

So by equating them, we can find  2 = 0.5