My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 9th, 2017, 01:38 PM   #1
Newbie
 
Joined: Oct 2017
From: Nowhere

Posts: 1
Thanks: 0

Unhappy Probability Distribution

I have attached the image of the problem.

I just do not understand how to proceed.

The question says you have "incomplete" distribution function because it only works for 0, 1, 2, and 3. To find the probability for 4, I know you need to apply "complement rule" (subtract all probabilities for 0, 1, 2, and 3 from 1). By definition, F(2) = P(X<=2), you need to be able to calculate P(X<=2) with f(x).

But I am very unsure on how to do this correctly. Everything I have tried so far has been wrong.

I do know how to get D and E as long as I can figure out how to get C.
Attached Images
File Type: jpg Screen Shot 2017-10-09 at 4.19.57 PM.jpg (11.1 KB, 6 views)
marissma is offline  
 
October 10th, 2017, 12:47 AM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 1,656
Thanks: 842

$X = \{0,1,2,3,4\}$

a)
$f[X] = \left\{\dfrac{1}{4},~\dfrac{3}{16}~,\dfrac{9}{64}, ~\dfrac{27}{256}\right\},~X=0,1,2,3$

$\displaystyle \sum_{X=0}^4 f[X] = 1 \Rightarrow f[4]=1-\dfrac{175}{256}=\dfrac{81}{256}=0.3164$

b)
$F(2)=\displaystyle \sum_{X=0}^2~f(X) = \dfrac{1}{4}+\dfrac{3}{16}+\dfrac{9}{64} = \dfrac{37}{64}=0.5781$

c)
$E[X] = \displaystyle \sum_{X=0}^4~X f(X)= \dfrac{525}{256}=2.051$

d)
$Var[X] = \displaystyle \sum_{X=0}^4~X^2 f(X) - \left(E[X]\right)^2=\dfrac{167511}{65536}=2.556$

e)
$SD[X] = \sqrt{Var[X]} = \dfrac{\sqrt{167511}}{256}=1.5988$
romsek is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
distribution, probability



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Stuck on probability distribution of a normal distribution problem faker97 Advanced Statistics 1 May 2nd, 2017 11:51 AM
Normal distribution: a probability distribution? froydipj Probability and Statistics 3 February 29th, 2016 05:35 PM
Which probability distribution is appropriate? Aqil Advanced Statistics 2 April 12th, 2011 02:07 PM
Probability Distribution Help? RossBrons Advanced Statistics 1 December 28th, 2008 09:35 AM
Probability Distribution Infiniti Advanced Statistics 3 November 5th, 2007 08:56 PM





Copyright © 2017 My Math Forum. All rights reserved.