estimator

[Sinistral]

what is the meaning of smaller bias? does it mean m1 has smaller bias compared to m2 => bias(m1)< bias(m2) OR m1 has smaller bias compared to m2 => mse(m1)< mse(m2)  ??

and also how to calculate E[ (ΣXi)^3  ]??

[Amit Goyal]

Here is the solution. Make sure you reason out every step.
estimator.png

[Sinistral]

mind blowing!!!
for calculating E[Xi^3] Mgf came to my rescue but the way you solved E[ (ΣXi)^3  ] was simply awesome. Leave alone unbiasedness of estimators, I learnt so many things just by seeing the way u calculated E[Xi^3] and E[ (ΣXi)^3  ].
thank you so much. :)

[duck]

Truly Amazing.. :) :)
Thank you Sir.. :)