Suppose that X sub 1, X sub 2,... X sub n and Y sub 1, Y sub 2,... Y sub n are independent random samples from populations with means mu sub x and mu sub y and variances sigma squared sub x and sigma squared sub y , respectively. Show that X bar - Y bar is a consistent estimator of mu sub x - mu sub y.(adsbygoogle = window.adsbygoogle || []).push({});

I know that the Bias and Variance must equal 0 so...

Bias (Xbar - Ybar) =

[E(Xbar) - mu sub x] - [E(Ybar) - mu sub y]

= 0

Variance (Xbar - Ybar)

[sigma squared sub x /n] - [sigma squared sub y /n]

= 0

I'm pretty sure this is incorrect.

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# Show that Xbar - Ybar is a consistent estimator

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