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Stat Notes Week 6

by: Emmy Thornsberry

Stat Notes Week 6 MATH 2600

Emmy Thornsberry
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About this Document

Includes - random variable notes - nCr and pCr notation and explanation - discrete and continuous random variables
Introduction To Statistics
James Baugh
Class Notes
Math, Statistics, variables




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This 2 page Class Notes was uploaded by Emmy Thornsberry on Wednesday September 21, 2016. The Class Notes belongs to MATH 2600 at Georgia College & State University taught by James Baugh in Fall 2016. Since its upload, it has received 18 views. For similar materials see Introduction To Statistics in Math at Georgia College & State University.


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Date Created: 09/21/16
Stat notes   9/21    nPr= n place r  ­ Use when the order of something is important and relevant.    nCr= n choose r   ­ Use when the order of something is irrelevant, but the overall result is relevant.     1.) A bag contains 10 colored balls, 5 red and 5 green. If you draw 3 without replacement,  what is the probability that all three are green?  ­ Order does not matter here so we’ll be using nCr   ­ 10C3 ways to draw 3 general balls out of the 10   ­ 5C3 to draw 3 green balls from the bag  ­ Poob(3 green balls)= 5C3/10C3= (5x4x3/3x2x1)/(10x9x8/3x2x1)= 1/12  ­ C means n(n­1)(n­2)... (n­r)     2.) You have 10 cards numbered 1­10. After shuffling, you place 3 in a row. What is the  probability of getting 3 in increasing sequence.  ­ Order matters here so we’ll be using nPr  ­ 10P3 ways to place 3 out of 10 in sequence  ­ 8 ways to draw 3 of 10 in increasing sequence   ­ (1,2,3)(2,3,4)(3,4,5)(4,5,6)(5,6,7)(6,7,8)(7,8,9)(8,9,10)  ­ (8/720)­(4/360)= 1/90    Discrete vs continuous random variables  ­ Look at sample space  ­ Discrete or continuous? If discrete, then random variable is discrete; if  continuous, then random variable is continuous.  ­ Sample space is a set of numbers  ­ A continuous set (sample size) is composed of intervals  ­ A discrete set (sample size) is composed of numbers separated by intervals (places and  spaces).   For X, a discrete random variable, the function f(x)=P(X=x)   Read; the function f of x is the probability that X is equal to x.   x is an algebraic variable. X is random variable.   Known as the probability distribution function (PDF).     x  2  3  4  5  6  7  8  9  10  11  12  P(X=x)  1/36  2/36  3/36  4/36  5/36  6/36  7/36  8/36  9/36  10/36  11/36  PDF of x=sum of 2 for dice.    Cumulative distribution function or CDF is  g(x)=P(X< ​ ​x).   P(X<​ ​ 0)=33/36 (found using the table above)  


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