S3 maths help!

Hi,
Can anyone explain question 2 a on this S3 paper,
http://pmt.physicsandmathstutor.com/download/Maths/A-level/S3/Papers-Edexcel/June%202014%20(IAL)%20QP%20-%20S3%20Edexcel.pdf
I dont understand the markscheme:
http://pmt.physicsandmathstutor.com/download/Maths/A-level/S3/Papers-Edexcel/June%202014%20(IAL)%20MS%20-%20S3%20Edexcel.pdf
Thank you!

Reply 1

old_engineer

11

Original post by examstudy

Hi,
Can anyone explain question 2 a on this S3 paper,
http://pmt.physicsandmathstutor.com/download/Maths/A-level/S3/Papers-Edexcel/June%202014%20(IAL)%20QP%20-%20S3%20Edexcel.pdf
I dont understand the markscheme:
http://pmt.physicsandmathstutor.com/download/Maths/A-level/S3/Papers-Edexcel/June%202014%20(IAL)%20MS%20-%20S3%20Edexcel.pdf
Thank you!

You could reasonably expect Xbar (a sample mean) to be an unbiased estimator for E(X) (the mean value of the theoretical model). But what is E(X) for U[a - 3, 2a + 3] ? Clue: it’s not a. So Xbar is an unbiased estimator for something other than a, therefore...

Reply 2

examstudy

OP

10

Original post by old_engineer

You could reasonably expect Xbar (a sample mean) to be an unbiased estimator for E(X) (the mean value of the theoretical model). But what is E(X) for U[a - 3, 2a + 3] ? Clue: it’s not a. So Xbar is an unbiased estimator for something other than a, therefore...

Thank you, I worked out that for X the mean was 3/2 a and then i was completely lost because how do I know that Xbar isn't also 3/2a. The question doesn't say that its a. This is where I am lost?

Reply 3

old_engineer

11

Original post by examstudy

Thank you, I worked out that for X the mean was 3/2 a and then i was completely lost because how do I know that Xbar isn't also 3/2a. The question doesn't say that its a. This is where I am lost?

Individual values of Xbar will vary from sample to sample. But if you took lots of independent samples and took the mean of the sample means, you would expect that to converge on 3a/2. Thus Xbar is an unbiased estimator for 3a/2, which means it’s a biased estimator for a.

Reply 4

examstudy

OP

10

Thank you very much for helping but I don't understand, where the a comes in?
I understand the mean of X is 3/2 a then i understand that Xbar would also be 3/2 a but then I just get lost, I don't understand why that means its a biased estimator of a? @old_engineer

(edited 5 years ago)

Reply 5

old_engineer

11

Original post by examstudy

Thank you very much for helping but I don't understand, where the a comes in?
I understand the mean of X is 3/2 a then i understand that Xbar would also be 3/2 a but then I just get lost, I don't understand why that means its a biased estimator of a? @old_engineer

Say we wanted an estimate for a based on a statistic derived from a sample. We have established that Xbar (for the sample) provides an unbiased estimate for 3a/2. At the same time we can also say that Xbar provides a biased estimate for a, and that the bias is 3a/2 - a.

The next part of the question then asks how we might use k(Xbar) as an unbiased estimator for a....

Reply 6

examstudy

OP

10

Ok... I think, sorry I'm new to this topic and have self taught so I think I haven't got everything quite figured out yet.
So this is how I'm understanding it: because Xbar is a unbiased estimate for the mean (of the population) it is equal to 3a/2, 3a/2 does not equal a and therefore Xbar doesn't equal a?
If Xbar doesn't equal a its not a unbiased estimator for it?
Am i along the right tracks, again thank you for your time.

Reply 7

old_engineer

11

Original post by examstudy

Ok... I think, sorry I'm new to this topic and have self taught so I think I haven't got everything quite figured out yet.
So this is how I'm understanding it: because Xbar is a unbiased estimate for the mean (of the population) it is equal to 3a/2, 3a/2 does not equal a and therefore Xbar doesn't equal a?
If Xbar doesn't equal a its not a unbiased estimator for it?
Am i along the right tracks, again thank you for your time.