Random Variables: Concept, Types, and Probability Distributions, Slides of Statistics

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Random Variable

• A rule that assigns a number to each outcome in the sample space is called a random variable. - Random Variables denoted by letters at the end of the alphabet: X,Y,Z.

Types of random variables

• Discrete: potential values separated points

on the number line

• generally counting
• Continuous: potential values fall in an

interval on number line

• generally measured

Probability Distributions; Discrete Variables

• For Discrete Random Variables we

assign probabilities to the discrete

points

 

 

 

allX

r

P x

P x

P x P X x

( ) 1

0 ( ) 1

( ) ( )

Summarizing probability distribution

• The mean (expected value) of a discrete

random variable is

• This is the average value of X if the experiment is performed an extremely large number of times.

 x  E ( X )   xP ( x )

• The variance of a discrete random variable is
• The standard deviation is

 (^) x^2^  (^)  x  x   x ^2 P ( x )   x^2 P ( x )   x^2

2  (^) x   x