00:01
Ok, so the linear combinations that are contrasts are those where the coefficients, the sum of the coefficients equals zero.
00:11
So here in part i, the sum of the coefficients is 1 plus 3 minus 4, which does equal zero.
00:19
In part ii, it's 0 .3 plus 0 .5 plus 0 .1 plus 0 .1, which equals 1, which is not zero.
00:29
So it's not ii.
00:31
And for part iii, we've got a third plus a third plus a third minus one, which does equal zero.
00:38
So it's i and ii are our contrasts.
00:43
Sorry, i and iii.
00:45
And then part b says give an unbiased estimator for each of the linear combinations.
00:49
So we know that the unbiased estimator for a mean is just the sample mean.
00:54
So mu i is going to be estimated by if we call the sample mean x bar i...