Question
upstudy study bank question image url

II. Find the mean, variance and the standard deviation of the probability distribution of
the random variable X if for .

Ask by Carter Robbins. in the Philippines
Jan 02,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Mean: 5.5
Variance: 8.25
Standard Deviation: ≈2.872

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

To find the mean , variance , and standard deviation of the random variable , which is uniformly distributed from 1 to 10, we start with the mean:

Since each , we have:
Next, to calculate the variance:
First, we find :
Now variance:
Finally, the standard deviation is:
So, the mean is , the variance is , and the standard deviation is approximately .

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