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?

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- Jan 3rd 2012, 02:13 PMILikeSerenaRe: 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, 02:36 PMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
- Jan 3rd 2012, 02:37 PMILikeSerenaRe: Guidance r.e. Chebyshev's Inequlity.
- Jan 3rd 2012, 02:42 PMILikeSerenaRe: 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, 02:45 PMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
- Jan 3rd 2012, 02:47 PMILikeSerenaRe: Guidance r.e. Chebyshev's Inequlity.
- Jan 3rd 2012, 02:58 PMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
- Jan 3rd 2012, 03:23 PMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
Eurgh I cant think right now, I must be missing something obvious.

- Jan 4th 2012, 07:20 AMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
I'm beat. (Thinking)

- Jan 4th 2012, 11:20 AMILikeSerenaRe: 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, 06:07 AMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
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, 09:55 AMILikeSerenaRe: 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, 10:57 AMWevans2303Re: Guidance r.e. Chebyshev's Inequlity.
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.........