My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
December 15th, 2016, 10:54 AM   #1
Joined: Dec 2016
From: Trinidad and Tobago

Posts: 5
Thanks: 0

Chebychev inequality

Hi people,

I got the following question
A random variable X has mean 3 and variance 1. Use Chebychev's inequality to obtain an upper bound for:
a. P(|X-3|≥1),
b. P(|X-3|≥2).
I tried to answer A
kq=1 that means k=1/q, therefore k²=1²/q² since the variance is 1
k²=1²/1² k²=1
Therefore the upper bound is
Somehow it feels wrong, can anyone help me?
yeaho26 is offline  
December 15th, 2016, 11:03 AM   #2
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 1,780
Thanks: 919

$P[|X-\mu| \geq k \sigma] \leq \dfrac {1}{k^2}$



$P[|X-3| \geq k] \leq \dfrac{1}{k^2}$

$P[|X-3|\geq 1] \leq \dfrac{1}{1^2}=1$

$P[|X-3| \geq 2] \leq \dfrac{1}{2^2} = \dfrac 1 4$
romsek is offline  
December 15th, 2016, 12:02 PM   #3
Joined: Dec 2016
From: Trinidad and Tobago

Posts: 5
Thanks: 0

Ok, Thanks so I was right.
One more question, can you maybe help me again?
Fifty-five percent of all students on a campus are in Humanities. If 150 students are selected at random, what is the probability that the proportion of Humanities students in this particular sample will be between 45% and 55%.
I did the following
Here comes where I´m not quite sure
15=kσ k=15/σ k=15/√σ² k=15/√37.25 k=0.1654
Is it correct? I thought I have to use 15 since thats the distnace form 82.5 to 67.5 and therefore the interval I´m interested in.
Thanks again
yeaho26 is offline  

  My Math Forum > College Math Forum > Advanced Statistics

chebychev, inequality

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Triangle Inequality: Prove Absolute Value Inequality StillAlive Calculus 5 September 2nd, 2016 11:45 PM
Inequality? xcrbprame87 Algebra 5 September 24th, 2013 09:04 AM
explicit formula for chebychev's method? gelatine1 Algebra 3 October 15th, 2012 10:36 AM
Is it by chebychev's inequality? Anton29 Advanced Statistics 18 December 5th, 2011 05:01 PM
How do you solve this? Chebychev's inequality steve123 Advanced Statistics 2 August 1st, 2010 06:28 PM

Copyright © 2018 My Math Forum. All rights reserved.