What is Chebyshev's Inequity and How can it Solve Probabilities?

[freezer]

Homework Statement

The random variable X has an unknown distribution with μ = 10 and σ^2 = 1.2. use Chebyshev's inequity to solve the following.

a) Find an upper bound on the probability that X deviates from its mean by at least 2
b) Find an upper bound on the probability that X deviates from its mean by at least 100.
c) Let D be the amount of deviation from the mean on X, and plot the bound values given by Chebyshev's inequity for 0 < D < 1000. Use a log scale on the y-axis.
d) What does D have to be to guarantee an upper bound of exactly 10^(-6) with Chebyshev's inequity?

Homework Equations

The Attempt at a Solution

I missed lecture the day this was presented and the subject is not in the textbook. I have watched several videos on the concept but they do not seem relevant to this question. I have read a few .edu sites on the matter but seem to be more about the k value. So my professor is out of town till and won't be back before this is due. Can someone give me some guidance on this problem?

 

[Ray Vickson]

Homework Statement

The random variable X has an unknown distribution with μ = 10 and σ^2 = 1.2. use Chebyshev's inequity to solve the following.

a) Find an upper bound on the probability that X deviates from its mean by at least 2
b) Find an upper bound on the probability that X deviates from its mean by at least 100.
c) Let D be the amount of deviation from the mean on X, and plot the bound values given by Chebyshev's inequity for 0 < D < 1000. Use a log scale on the y-axis.
d) What does D have to be to guarantee an upper bound of exactly 10^(-6) with Chebyshev's inequity?

Homework Equations

The Attempt at a Solution

I missed lecture the day this was presented and the subject is not in the textbook. I have watched several videos on the concept but they do not seem relevant to this question. I have read a few .edu sites on the matter but seem to be more about the k value. So my professor is out of town till and won't be back before this is due. Can someone give me some guidance on this problem?

Show your work. I cannot believe you can do absolutely nothing with any of this problem. There are loads of websites available that go through this material, some in great detail and with worked examples.

 

[freezer]

Show your work. I cannot believe you can do absolutely nothing with any of this problem. There are loads of websites available that go through this material, some in great detail and with worked examples.

Ray,

I understand that some tutors get a rush when they get the opportunity to denigrate a student and pump-up their own ego through condescending remarks that serve little purpose. Hopefully, I have given you the opportunity to get that off your chest. Now that we are past that, I am not asking for you to give me the answer to the problem. However, a link would be helpful to one of the "loads of websites" that you found that would provide me guidance on how to solve this problem would be appreciated. The multitude of sites I have explored have not presented the needed information, or at least in a manner I find relevant to this problem.

Thank you for your generous help,
Rod

 

[Pythagorean]

Hi freezer. I just googled Chebyshev's inequality and I see lots of resources. I don't find Ray's post to be egotistical, I think he's just trying to help you help yourself rather than help you out right... which is to your benefit in the long term.

 

[freezer]

Hi freezer. I just googled Chebyshev's inequality and I see lots of resources. I don't find Ray's post to be egotistical, I think he's just trying to help you help yourself rather than help you out right... which is to your benefit in the long term.

Pythagorean,

Thanks for your reply. I to googled the key word but was more overwhelmed with the information and was having trouble applying it to this particular problem. I was looking at this source:

"www.ams.sunysb.edu/~jsbm/courses/311/cheby.pdf"

I was thinking it would be one sided setup. However, it seems to find the bounds, you need to know the type of distribution.

 

[haruspex]

Pythagorean,

Thanks for your reply. I to googled the key word but was more overwhelmed with the information and was having trouble applying it to this particular problem. I was looking at this source:

"www.ams.sunysb.edu/~jsbm/courses/311/cheby.pdf"

I was thinking it would be one sided setup. However, it seems to find the bounds, you need to know the type of distribution.

freezer, the very first equation at that link gives you exactly what you need to answer (a) and (d) immediately. You don't need to read the rest of the text.