Math Question Help (1 Viewer)

frankfurt

New Member
Joined
Sep 13, 2020
Messages
18
Gender
Female
HSC
2020
Hi Guys,

I came across this question that I'm struggling with:
Screen Shot 2022-06-14 at 9.28.48 pm.png

Please help.

Thanks in advance!
 

cossine

Well-Known Member
Joined
Jul 24, 2020
Messages
586
Gender
Male
HSC
2017
Hi Guys,

I came across this question that I'm struggling with:
View attachment 35815

Please help.

Thanks in advance!
The theorem mention is very similar to Markov's Inequality, however the integral on the right-hand-side has a lower-bound of x instead of zero.

I think it might be interesting to see if the theorem is actually true so maybe test some probability density function on it such as exponential or beta distribution.

Edit:

The theorem is true just take a look at the proof of Markov Inequality, "Probability Theoretic Approach": "Method 1". You should be able to use part of the proof.

https://en.wikipedia.org/wiki/Markov's_inequality
 
Last edited:

frankfurt

New Member
Joined
Sep 13, 2020
Messages
18
Gender
Female
HSC
2020
The theorem mention is very similar to Markov's Inequality, however the integral on the right-hand-side has a lower-bound of x instead of zero.

I think it might be interesting to see if the theorem is actually true so maybe test some probability density function on it such as exponential or beta distribution.

Edit:

The theorem is true just take a look at the proof of Markov Inequality, "Probability Theoretic Approach": "Method 1". You should be able to use part of the proof.

https://en.wikipedia.org/wiki/Markov's_inequality
Yeah I had a similar thought to use Markov's inequality. However, it's difficult to get rid of the integral of xf(x) from 0 to a in the example above. How would you go about doing that?
 

cossine

Well-Known Member
Joined
Jul 24, 2020
Messages
586
Gender
Male
HSC
2017
Yeah I had a similar thought to use Markov's inequality. However, it's difficult to get rid of the integral of xf(x) from 0 to a in the example above. How would you go about doing that?
So if take a look at the proof that should give you insight. There is chain of inequalities in proof 1. You should find integral of xf(x) from x to infinity there.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top