Question
upstudy study bank question image url

  1. Answer the following questions.
    A random variable has a mean 8 , a variance 9 , and an unknown probability
    distribution. Using Chebyshev’s theorem, find the lower bound of
    .

Ask by West Warner. in Pakistan
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The lower bound of is 0.25.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

Chebyshev’s theorem tells us that for any random variable, the proportion of observations that lie within standard deviations of the mean is at least . In this case, the mean and the variance , so the standard deviation .
To find , we consider which is equivalent to . Here, we define as the number of standard deviations:
.
Now applying Chebyshev’s theorem:
Thus, the probability of being outside that range is:
So, the lower bound of is at least .

Related Questions

Latest Probability Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy