# Guidance r.e. Chebyshev's Inequlity.

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• Jan 3rd 2012, 03:13 PM
ILikeSerena
Re: Guidance r.e. Chebyshev's Inequlity.
Erm... I meant which of Pr(1 ≤ X ≤ 17) and Pr(1 ≤ X ≤ 19) has to be the biggest?
The one covers more values of X than the other.
What does that say about which one is the bigger one?
• Jan 3rd 2012, 03:36 PM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by ILikeSerena
Erm... I meant which of Pr(1 ≤ X ≤ 17) and Pr(1 ≤ X ≤ 19) has to be the biggest?
The one covers more values of X than the other.
What does that say about which one is the bigger one?

Pr(1 ≤ X ≤ 19) covers more values of X.

I still don't know if I understand what you mean. (Doh)
• Jan 3rd 2012, 03:37 PM
ILikeSerena
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by Wevans2303
Pr(1 ≤ X ≤ 19) covers more values of X.

Yes, so Pr(1 ≤ X ≤ 19) ≥ Pr(1 ≤ X ≤ 17) > 0.86.

What does that tell you about the highest minimum value that you can find for Pr(1 ≤ X ≤ 19)?
• Jan 3rd 2012, 03:42 PM
ILikeSerena
Re: Guidance r.e. Chebyshev's Inequlity.
Errm.

If we split up the interval for X into 2 disjoint intervals we get:
Pr(1 ≤ X ≤ 19) = Pr((1 ≤ X ≤ 17) ∨ (17 < X ≤ 19))

Application of the sum rule for disjoint events gives us:
Pr((1 ≤ X ≤ 17) ∨ (17 < X ≤ 19)) = Pr(1 ≤ X ≤ 17) + P(17 < X ≤ 19)

So Pr(1 ≤ X ≤ 19) ≥ Pr(1 ≤ X ≤ 17).
• Jan 3rd 2012, 03:45 PM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by ILikeSerena
Yes, so Pr(1 ≤ X ≤ 19) ≥ Pr(1 ≤ X ≤ 17) > 0.86.

What does that tell you about the highest minimum value that you can find for Pr(1 ≤ X ≤ 19)?

I thought we worked out Pr(1 ≤ X ≤ 19) = 0.8 which is less than 0.86... (Crying)(Headbang)
• Jan 3rd 2012, 03:47 PM
ILikeSerena
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by Wevans2303
I thought we worked out Pr(1 ≤ X ≤ 19) = 0.8 which is less than 0.86... (Crying)(Headbang)

Well, we used 2 different methods to find a lower bound for Pr(1 ≤ X ≤ 19).

The two-tailed version gave us Pr(1 ≤ X ≤ 19) > 0.86, while the one-tailed version gave us Pr(1 ≤ X ≤ 19) > 0.8.

Both inequalities are true.
• Jan 3rd 2012, 03:58 PM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by ILikeSerena
Well, we used 2 different methods to find a lower bound for Pr(1 ≤ X ≤ 19).

The two-tailed version gave us Pr(1 ≤ X ≤ 19) > 0.86, while the one-tailed version gave us Pr(1 ≤ X ≤ 19) > 0.8.

Both inequalities are true.

Right okay I understand that bit.

One sec let me ponder.
• Jan 3rd 2012, 04:23 PM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
Eurgh I cant think right now, I must be missing something obvious.
• Jan 4th 2012, 08:20 AM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
I'm beat. (Thinking)
• Jan 4th 2012, 12:20 PM
ILikeSerena
Re: Guidance r.e. Chebyshev's Inequlity.
Well, I'll help you, but you will have to show some of your thought processes if you want that...
Otherwise, I have no clue which obvious thing it is that you are missing.
• Jan 5th 2012, 07:07 AM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by ILikeSerena
Well, I'll help you, but you will have to show some of your thought processes if you want that...
Otherwise, I have no clue which obvious thing it is that you are missing.

I'm just a little lost in the question I think.

So we did a two tailed inequality and got 0.86.

Then a one tailed version to get 0.80.

Now are we trying to find the final answer? Can you explain why 0.80 is not the answer? Isn't that what the question is asking for?

I don't understand what you mean when you say 'highest minimum value'.

Thanks for helping me and im sorry for being tough.
• Jan 5th 2012, 10:55 AM
ILikeSerena
Re: Guidance r.e. Chebyshev's Inequlity.
0.80 is a correct answer and so is 0.86.

Since Chebyshev gives an upper estimate of the tails and the upper estimate of 0.14 for the tails is sharper than the upper estimate of 0.20.
This means that 0.86 is a better answer, although 0.80 is also a correct answer.
• Jan 6th 2012, 11:57 AM
Wevans2303
Re: Guidance r.e. Chebyshev's Inequlity.
Quote:

Originally Posted by ILikeSerena
0.80 is a correct answer and so is 0.86.

Since Chebyshev gives an upper estimate of the tails and the upper estimate of 0.14 for the tails is sharper than the upper estimate of 0.20.
This means that 0.86 is a better answer, although 0.80 is also a correct answer.

Cool, this is the closest I came, my reasoning was that 0.14 < 0.20 so 0.86 is the answer to use, is that some what a correct thought process or have I come to the correct conclusion by chance?

Not sure what you mean by tails you see.

:)

EDIT: Oh no I do know what tails are.........
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