Statistics Question

Okay,

I have Xbar~N(5,0.5) , n=50 (n=no. samples)

Ybar~N(10,0.25), n=150 (n=no. samples)

How do i find the average of the mean and std devs of the 2 averages? I know mean would be (5x50+10x150)/(50+150), but how about variance?

Hi,

1. Find the mean (i.e., 50 x 5)

and variance of X_1 + ... + X_50 (i.e., 50^2 x 0.5) where

X_1 + ... + X_50 = 50 X-bar.

2. Find the mean and variance of Y_1 + ... + Y_150 where

Y_1 + ... + Y_150 = 150 Y-bar.

3. Find the mean of (X_1 + ... + X_50 + Y_1 + ... + Y_150) / 200 which you have done so (excellent!).

4. Find the variance of (X_1 + ... + X_50 + Y_1 + ... + Y_150) / 200 which is

{ Var (X_1 + ... X_50) + Var (Y_1 + ... + Y_150) } / { 200^2 }.

Thanks.

Cheers,
Wen Shih