Chebyshevs inequality question!

the greatest

14

jokes

(edited 12 years ago)

Reply 1

DFranklin

18

If you've covered it, I would use the 1 sided version of Chebyshev's inequality

Reply 2

the greatest

OP

14

Original post by DFranklin

If you've covered it, I would use the 1 sided version of Chebyshev's inequality

Our teacher gave us a very very brief intro into the inequality, purpose for upper bounds closely related to the mean etc

All I know is I have to find E(x) and var(x), and as well, I dont think this question invloves sample mean as inital question says T as opposed to Sample T

Im struggling, as it was a 5 min job in the last lecture! :s-smilie:

Reply 3

DFranklin

18

So, have you covered the 1-sided version of the inequality?

Reply 4

the greatest

OP

14

Original post by DFranklin

So, have you covered the 1-sided version of the inequality?

nope, she gave us an example involving multiple choice but it was using possion distibution as well, like eg probability you pass an exam with 10 questions given 40% is pass rate, and another with 100 questions invloving chebyshevs equations, that is all

:s-smilie:

Reply 5

DFranklin

18

Well, in that case I can't really see a better option than observing that P(T >=110) <= P(|T-80|>=30), and you can give an upper bound for this 2nd probability using the normal two-sided Cheybyshev inequality.

Reply 6

the greatest

OP

14

Original post by DFranklin

Well, in that case I can't really see a better option than observing that P(T >=110) <= P(|T-80|>=30), and you can give an upper bound for this 2nd probability using the normal two-sided Cheybyshev inequality.

ok, btw y -80 as opposed to -20,30 etc, im very wary on this topic

Reply 7

DFranklin

18

The inequality is in your signature - it shouldn't be hard to work it out which term in the inequality corresponds to which term in P(|T-80|>=30).

Reply 8

the greatest

OP

14

yes i see that its (30)^2 at the bottom! but why 30 im asking?

Reply 9

the greatest

OP

14

Original post by DFranklin

The inequality is in your signature - it shouldn't be hard to work it out which term in the inequality corresponds to which term in P(|T-80|>=30).

yes i see that its (30)^2 at the bottom! but why 30 im asking?

Reply 10

DFranklin

18

Original post by the greatest

yes i see that its (30)^2 at the bottom! Nope. Did you forget about

\sigma

?

What is the random variable you're working with here? (Answer: T).

So we have

\mathbb{P}(|T-\mu| \geq k \sigma) \geq \frac{1}{k^2}

So, what's

\mu

? What's

\sigma

? etc. etc.

Reply 11

the greatest

OP

14

mew being the E(X) and sigma being standrad deviation?

Reply 12

the greatest

OP

14

Original post by DFranklin

Nope. Did you forget about

\sigma

?

What is the random variable you're working with here? (Answer: T).

So we have

\mathbb{P}(|T-\mu| \geq k \sigma) \geq \frac{1}{k^2}

So, what's

\mu

? What's

\sigma

? etc. etc.

mew being E(T) and sigma being SD??

Reply 13

DFranklin

18

I have to ask why you've put an equation in your sig if you don't understand it?

Edit: (to be clear, what you've said above is not wrong, but you shouldn't need to ask me whether it's right if you've done anything at all about Chebyshev's inequality).