My Math Forum  

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

Advanced Statistics Advanced Probability and Statistics Math Forum


Thanks Tree1Thanks
  • 1 Post By romsek
Reply
 
LinkBack Thread Tools Display Modes
June 20th, 2017, 03:06 PM   #1
Member
 
Joined: Apr 2017
From: PA

Posts: 45
Thanks: 0

Find a, b, and c if µ(X) = 0, σ^2(X) = 1/15

Let X be a random variable with range [−1,1] and density function f = ax^2 + bx + c if |x| < 1 and 0 otherwise.

(d) Find a, b, and c if µ(X) = 0, σ^2(X) = 1/15, and sketch the graph of fX(x) .

for this, I thought about taking the definite integral of ∫(ax^2+bx+c)dx from -1 to 1, to get (a/3)+(b/2)+c+(a/3)+(-b/2) to eventually get ((2a)/3)+2c=0. Then, I thought about getting a by itself to get a=-3c, and for b, since they canceled, I would have to say that B may not exist. Also, as for C, I got (-a/3), how should you find a, b, and c?
poopeyey2 is offline  
 
June 20th, 2017, 11:41 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,607
Thanks: 819

you have 3 equations for the 3 unknowns

$f(x) = a x^2 + b x + c$

$\displaystyle \int \limits_{-1}^1 ~f(x) ~dx = 1$

$\displaystyle \int \limits_{-1}^1 ~xf(x) ~dx = 0$

$\displaystyle \int \limits_{-1}^1 ~x^2 f(x) ~dx = \dfrac{1}{15}$

these should be relatively straightforward to expand and solve.

yell back if you need further assistance.
Thanks from poopeyey2
romsek is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
1 or 15, µx, find, σ2x



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find The Density of the body to find fat precentage harryp Algebra 2 September 8th, 2015 09:11 PM
find sin27 and find 63 mared Trigonometry 3 July 2nd, 2014 09:09 AM
Find Sk and Find Kv ( i got example formula below) kingkos Algebra 5 November 25th, 2012 12:40 AM
I want to find the distance in algebra find it kevinman Algebra 8 March 8th, 2012 06:53 AM





Copyright © 2017 My Math Forum. All rights reserved.