Edexcel S3 - Wednesday 25th May AM 2016

The key thing is understanding the difference between adding multiple distributions (it's usually men and women's weight or stuff like that) and multiplying one distribution.

Eg if M~N(a,b) and W~N(c,d) then the difference between a man and a woman's weight would be ~N(a-c, b+d) but if you were asked for the probability of a man's height being 1.5 times more than a woman's, you'd be looking for something like (D :=M-1.5W)~N(a-1.5c,b+2.25d) and you'd find P(D>0) and.. that's about it.

Is it with decimals/fractions that we square?

The key thing is understanding the difference between adding multiple distributions (it's usually men and women's weight or stuff like that) and multiplying one distribution.

Eg if M~N(a,b) and W~N(c,d) then the difference between a man and a woman's weight would be ~N(a-c, b+d) but if you were asked for the probability of a man's height being 1.5 times more than a woman's, you'd be looking for something like (D :=M-1.5W)~N(a-1.5c,b+2.25d) and you'd find P(D>0) and.. that's about it.

The problem I have is with $\displaystyle Var(aX) = a^{2}Var(X)$

If $\displaystyle Var(X + Y + Z) = Var(X) + Var(Y) + Var(Z)$

Then why is $\displaystyle Var(3X) = Var(X + X + X) \neq 3Var(X)$

I think physicsmaths and Zacken discussed this in the first 10 posts, but I still don't understand

Are you asking why can't we split Var(X+X) into Var(X)+Var(X) just like we can Var(X+Y)?

The problem I have is with $\displaystyle Var(aX) = a^{2}Var(X)$

If $\displaystyle Var(X + Y + Z) = Var(X) + Var(Y) + Var(Z)$

Then why is $\displaystyle Var(3X) = Var(X + X + X) \neq 3Var(X)$

I think physicsmaths and Zacken discussed this in the first 10 posts, but I still don't understand

Var(3X) is not qual to Var(X + X + X)
Var(3X) will give you 3^2Var(X)
BUT Var(X+X+X) Will give you 3Var(X)

Yeah I think so

Var(3X) is not qual to Var(X + X + X)
Var(3X) will give you 3^2Var(X)
BUT Var(X+X+X) Will give you 3Var(X)

The problem I have is with $\displaystyle Var(aX) = a^{2}Var(X)$

If $\displaystyle Var(X + Y + Z) = Var(X) + Var(Y) + Var(Z)$

Then why is $\displaystyle Var(3X) = Var(X + X + X) \neq 3Var(X)$

I think physicsmaths and Zacken discussed this in the first 10 posts, but I still don't understand

If you substitute X and Y with X1 and X2 respectively, where they both have the same distribution as X,

You see how X1+X2 has a very different distribution from X+X? They both have the same mean, but the variance is different.

Districution aint X it is X_i. So districution of 3X is different to X_i.Posted from TSR Mobile

Surely if they have the same distribution as X then they are equal to X? How does that work?



I'm slowly getting there with understanding though. So when we have the sample variable which has a multiple like $Var(5X_1) = 25Var(X_1)$ but when there are multiple variables combined like $Var(X_1 + 2X_2) = Var(X_1) + 4Var(X_2)$ we get squares because combinations of X are distinct from combinations of $X_i$'s



Ah yeah because one's scaled up, Zacken's early comment makes loads of sense now.

Thanks to both of you

Surely if they have the same distribution as X then they are equal to X? How does that work?

They have the same distribution yes, but they don't have to be equal. They are different random variables, so X1 could be equal to 2 while X2 equal to 7. Just like X and Y are different. This is why I tried to highlight the fact that the probability of getting 2a is different depending on if we had X+X (same variable added to itself) or if we had X1+X2 (different variables added).

Normal distribution if you're not very confident with it

Otherwise it took me around 5 hours to study from scratch, the bulk of that being chapter 2 tbh

Posted from TSR Mobile

Cheers yeah, just been refreshing my memory on normal distribution.

And wow, 5 hours!? How did you go through so quickly?

https://www.youtube.com/user/jbstatistics

I didn't practice at all though, straight into the 2000 paper. Going back now and practicing some of the chapters (1 and 2)

Hello Sean,
I have got a S3 question, if you are able to answer it?

it's a question about goodness of fit( continuous uniform distribution)
In the S3 text book, there is an example of it,but when I looked at it,I got a little bit confused about how they didn't combine cells with expected frequencies less than 5, my question is :is that always the case just for continuous uniform distribution or was it a mistake in the text book?
It would be great and helpful if you can answer it for me.
Thanks.

As far as I am aware there is nothing special about continuous uniform distributions so I would say that it is most likely a mistake.