Hey! Sign in to get help with your study questionsNew here? Join for free to post
 You are Here: Home >< Maths

# S3

Announcements Posted on
Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
1. https://771a1ec81340d97ae9ed29694f73...XZCVmc/CH1.pdf

On Page 10, for part d the summation part, I have that it is 30 by doing

3 * (Var(Y)+0.25Var(X)

So I get 3(9+2) = 33 which does not match solution

Is it not this way, they use Y1+y2 etc.
2. (Original post by L'Evil Wolf)
https://771a1ec81340d97ae9ed29694f73...XZCVmc/CH1.pdf

On Page 10, for part d the summation part, I have that it is 30 by doing

3 * (Var(Y)+0.25Var(X)

So I get 3(9+2) = 33 which does not match solution

Is it not this way, they use Y1+y2 etc.
Puzzled as to why you're multiplying the Var(X) by 3.

Hence
3. (Original post by ghostwalker)
Puzzled as to why you're multiplying the Var(X) by 3.

Hence
How come it is not (Y1-0.5X)+(Y2-0.5X)+(Y3-0.5X)?
4. (Original post by L'Evil Wolf)
How come it is not (Y1-0.5X)+(Y2-0.5X)+(Y3-0.5X)?
I added an extra line to my previous post.

It's not what you've just posted because of the way S is defined. There's only one lot of X involved.
5. (Original post by L'Evil Wolf)
How come it is not (Y1-0.5X)+(Y2-0.5X)+(Y3-0.5X)?
The summation sign only applies to what's immediately following.

6. (Original post by ghostwalker)
I added an extra line to my previous post.

It's not what you've just posted because of the way S is defined. There's only one lot of X involved.
ah because X is not changing right?

thanks you for your help
7. (Original post by L'Evil Wolf)
ah because X is not changing right?

thanks you for your help
Added a second post above.

It's not because the X isn't changing.

It's really an extension of BIDMAS, or BODMAS or whatever you use. The summation is effectively a function, like log or cosine, etc.

log 6 + 7 means (log 6) + 7, not log (6+7)
8. (Original post by ghostwalker)
The summation sign only applies to what's immediately following.

Thank you very much I now understand.
9. (Original post by L'Evil Wolf)
Thank you very much I now understand.
10. (Original post by ghostwalker)
The summation sign only applies to what's immediately following.

I know this is a while after lol but:

S = Yi - 0.5X + Y2-0.5X + Y3 - 0.5X

= 3[Yi - 0.5X]

= 3Var(Yi)+0.25Var(X)

which still yields 28 in that regard!

So it is a conincindence that both ways that you stated result in the same answer?
11. (Original post by L'Evil Wolf)
I know this is a while after lol but:

S = Yi - 0.5X + Y2-0.5X + Y3 - 0.5X

= 3[Yi - 0.5X]

= 3Var(Yi)+0.25Var(X)

which still yields 28 in that regard!

So it is a conincindence that both ways that you stated result in the same answer?
How did you go from the first bolded line to the second bolded line?
12. (Original post by Zacken)
How did you go from the first bolded line to the second bolded line?
Took a factor of 3 out and then applied the variance of it. I assume you consider it to be wrong?

The idea stemmed from integration, how we take out constants and then integrate if that makes sense?
13. (Original post by L'Evil Wolf)
Took a factor of 3 out and then applied the variance of it. I assume you consider it to be wrong?

The idea stemmed from integration, how we take out constants and then integrate if that makes sense?
By that logic, why don't you "take out the 0.5 and then applied the variance of X"?
14. (Original post by Zacken)
By that logic, why don't you "take out the 0.5 and then applied the variance of X"?
Do you mean, have:

3[Yi - 0.5X]

3/2[2Yi - X]

3/2[ 4Var(Yi) + Var(X)]

3/2 [4(9)+4]

3/2[40}
=60

which would be incorrect.
15. (Original post by L'Evil Wolf)
Do you mean, have:

3[Yi - 0.5X]

3/2[2Yi - X]

3/2[ 4Var(Yi) + Var(X)]

3/2 [4(9)+4]

3/2[40}
=60

which would be incorrect.
No, I'm saying, why are you doing:

Var(3(Yi - 0.5X)) = 3Var(Yi - 0.5X).
16. (Original post by Zacken)
No, I'm saying, why are you doing:

Var(3(Yi - 0.5X)) = 3Var(Yi - 0.5X).
I was doing from concepts of integration, as in the factoring out a constant, but this wouldn't apply in this different mathematical operation.
17. (Original post by L'Evil Wolf)
I was doing from concepts of integration, as in the factoring out a constant, but this wouldn't apply in this different mathematical operation.
I'm afraid I don't understand your point, but Ghostwalker's way is the correct version and yours is simply an (incorrect) fluke.
18. (Original post by Zacken)
I'm afraid I don't understand your point, but Ghostwalker's way is the correct version and yours is simply an (incorrect) fluke.
Okay, thank you/
19. (Original post by L'Evil Wolf)
I know this is a while after lol but:

S = Yi - 0.5X + Y2-0.5X + Y3 - 0.5X
OK, you're using the second definition of S (not the one in the original question)

= 3[Yi - 0.5X]
This is meaningless; with the Yi, rather than Y1+Y2+Y3

If you're going to follow through with the second definition, you'd have:

S=Y1+Y2+y3 - 1.5X

assuming we're dealing with just one observation of X, and not three independent ones.

Working out the variance you'd have:

Var(S) = Var(Y1)+Var(Y2)+Var(Y3)+2.25Var( X)

= 3 Var(Y) + 2.25Var(X)

which won't yield 28.

IF you had three independent observations of X instead; i.e. X1,X2,X3, you'd get

S=Y1+Y2+y3 - 0.5X1-0.5X2-0.5X3

Then Var(S) = Var(Y1)+Var(Y2)+Var(Y3)+0.25Var( X1)+0.25Var(X2)+0.25Var(X3)

=3Var(Y)+0.75Var(X)

Again, no 28.
20. (Original post by ghostwalker)
OK, you're using the second definition of S (not the one in the original question)

This is meaningless; with the Yi, rather than Y1+Y2+Y3

If you're going to follow through with the second definition, you'd have:

S=Y1+Y2+y3 - 1.5X

assuming we're dealing with just one observation of X, and not three independent ones.

Working out the variance you'd have:

Var(S) = Var(Y1)+Var(Y2)+Var(Y3)+2.25Var( X)

= 3 Var(Y) + 2.25Var(X)

which won't yield 28.

IF you had three independent observations of X instead; i.e. X1,X2,X3, you'd get

S=Y1+Y2+y3 - 0.5X1-0.5X2-0.5X3

Then Var(S) = Var(Y1)+Var(Y2)+Var(Y3)+0.25Var( X1)+0.25Var(X2)+0.25Var(X3)

=3Var(Y)+0.75Var(X)

Again, no 28.
Oh right, yes. Thank you.

Write a reply…

Submit reply

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
that username has been taken, please choose another Forgotten your password?
2. this can't be left blank
this email is already registered. Forgotten your password?
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. Oops, you need to agree to our Ts&Cs to register
2. Slide to join now Processing…

Updated: May 1, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### University open days

Is it worth going? Find out here

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.