Chebyshev's Inequality: Given fixed k>1, fixed mu, fixed sigma>0, find g(x) so that

[BlueSourBalls]

Chebyshev's Inequality: Given fixed k>1, fixed mu, fixed sigma>0, find g(x) so that

If there's anyone willing to help me out on this Chebyshev's inequality problem, please try question 1. Everything below the question is just information/tips on how to do it. Thank you

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1. Given a fixed real number \(\displaystyle k\, >\, 1,\) any fixed real number \(\displaystyle \mu,\) and any fixed real number \(\displaystyle \sigma\, >\, 0,\) find a probability density function \(\displaystyle g(x)\) such that a continuous random variable \(\displaystyle X\) with this density will have \(\displaystyle E(X)\, =\, \mu,\) standard deviation \(\displaystyle \sqrt{V(X)\,}\, =\, \sigma,\) and satisfy the following:

. . . . .\(\displaystyle P\left(\big|X\, -\, \mu\big|\, \geq\, k\sigma \right)\, =\, \dfrac{1}{k^2}\)

 

[tkhunny]

If only it weren't so small and if only you had shown some of your work and provided some of your thoughts?

Please give us something to work with.

 

[Steven G]

If there's anyone willing to help me out on this Chebyshev's inequality problem, please try question 1. Everything below the question is just information/tips on how to do it. Thank you
View attachment 9341

Strange but the image that came up was the biggest clearest image I have ever seen on this forum. More importantly where are you stuck? If you show us what you tried doing, then someone will guide you through the problem We just need to see where you are stuck. Fair enough?

 

[tkhunny]

Strange but the image that came up was the biggest clearest image I have ever seen on this forum.

Not strange at all. It's called improvement and replacement by the OP.

 

[BlueSourBalls]

Strange but the image that came up was the biggest clearest image I have ever seen on this forum. More importantly where are you stuck? If you show us what you tried doing, then someone will guide you through the problem We just need to see where you are stuck. Fair enough?

I just no have clue on where to start. My professor suggested to begin with choosing "easier" integers for k, mu, and sigma values. For example, E(X)=mu=0, sigma=1, k=2; which were the exact integers that he suggest.

I understand that I cannot receive a full walk through of the answer, but I was just hoping for some sort of beginning step for me to work with if that was possible. I have to create some continuous density function with these values to satisfy the given inequality.

I completely understand if you are unable to help due to my lack of initial work, but I do appreciate the reply to the thread nonetheless!