Edexcel S3 - Wednesday 25th May AM 2016

Statistic = If X1,X2,X3,...,Xn is a random sample of size n from some population, then a statistic T is a random variable consisting of any function of the Xi that involves no other unknown quantities. A stastic must not contain any unknown population paramaters.

Is that okay? Or words to that effect



Lol

That sounds great.


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Statistic = If X1,X2,X3,...,Xn is a random sample of size n from some population, then a statistic T is a random variable consisting of any function of the Xi that involves no other unknown quantities. A stastic must not contain any unknown population paramaters.

Is that okay? Or words to that effect



Lol

Sounds fine to me. So anything involving mu, lambda, lowercase sigma.. isn't one

what does lambda represent.

sigma squared would aslso not be a statistic if used to represent variance?

Lambda is a rate parameter, at A-level it is commonly associated with the Poisson distribution.

I don't think so, if the variance were unknown. If the variance were known.. I seem to remember the definition of a statistic being something that is solely calculated from the observations (i.e doesn't involve variance or anything other than observations) but that'd be in the book somewhere.

Last question on this pls explain why 10 and not 10mu

What you've done is slightly messy.

To illustrate a point, what you've got for E(Y) is correct, but what you really did was...

Y = sum of those things which is correct.

Since xi's are independent, identically distributed, this means that E(Y) = E(10*(x1-mu)/sd), and so using laws of expectation that gives 10*E(x1-mu)/E(sd) = 10 * (E(x1) - E(mu)) / E(sd)) = 10 * (mu - mu)/sd = 0.

The problem is that you've changed Var(x1 - mu / sd) into Var ( var(x1) - mu / sd) which doesn't quite make sense - can you see what to do instead with your method? (It works, but it is very easy to make a mistake with it)

Thank you, this was helpful.

Do you understand how you use your method for finding Var(Y) now?

Sorry but I still end up with 10sigma^2/sigma giving me 10 sigma :/

With the method you originally posted?

Yes similarly.

I get that variance(mean) = 0

It is the Var(Xi/sigma) which I don't get, is the var(Xi) not simply sigma^2.

It obviously is sigma I suppose from the answer?

Looking at your answer - starting from the line Var(Y). The next 3 lines - all the sigma1/2s's should still be x1's /x2s etc as you should not have applied Var yet.

Keep the xi's there until line 4, where everything else is correct, giving you 10Var((xi/sigma)-(mu/sigma)).

This is now where you apply Variance, as it is of the form Var(aX+c), where a is 1/sigma and c is mu/sigma. And Var(aX+c) = a^2Var(x).. and the rest should follow.

Thank you for doing this.

omg how were you supposed to figure that sigma was a number/constant? Was it that they said the standard wdeviation was sigma in the question?

sigma is a constant in this situation, not a variable.

mu/sigma is a number when you specify what mu / sigma are, eg mu = 5 sigma = 2.

Hi, does anyone know please whether we could be asked to prove example 7 in the exam? Thanks