- #1
birdec
- 5
- 0
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.
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.
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.