PPT: Random Variables | Engineering Mathematics - Civil Engineering (CE) PDF Download

 Page 1


3-2 Random Variables
• In an experiment, a measurement is usually  
denoted by a variable such as X. 
• In a random experiment, a variable whose 
measured value can change (from one replicate of 
the experiment to another) is referred to as a 
random variable.
Page 2


3-2 Random Variables
• In an experiment, a measurement is usually  
denoted by a variable such as X. 
• In a random experiment, a variable whose 
measured value can change (from one replicate of 
the experiment to another) is referred to as a 
random variable.
3-2 Random Variables
Page 3


3-2 Random Variables
• In an experiment, a measurement is usually  
denoted by a variable such as X. 
• In a random experiment, a variable whose 
measured value can change (from one replicate of 
the experiment to another) is referred to as a 
random variable.
3-2 Random Variables 3-3 Probability
• Used to quantify likelihood or chance
• Used to represent risk or uncertainty in engineering
applications
•Can be interpreted as our degree of belief or 
relative frequency
Page 4


3-2 Random Variables
• In an experiment, a measurement is usually  
denoted by a variable such as X. 
• In a random experiment, a variable whose 
measured value can change (from one replicate of 
the experiment to another) is referred to as a 
random variable.
3-2 Random Variables 3-3 Probability
• Used to quantify likelihood or chance
• Used to represent risk or uncertainty in engineering
applications
•Can be interpreted as our degree of belief or 
relative frequency
3-3 Probability
• Probability statements describe the likelihood that 
particular values occur. 
• The likelihood is quantified by assigning a number 
from the interval [0, 1] to the set of values (or a 
percentage from 0 to 100%). 
• Higher numbers indicate that the set of values is 
more likely.
Page 5


3-2 Random Variables
• In an experiment, a measurement is usually  
denoted by a variable such as X. 
• In a random experiment, a variable whose 
measured value can change (from one replicate of 
the experiment to another) is referred to as a 
random variable.
3-2 Random Variables 3-3 Probability
• Used to quantify likelihood or chance
• Used to represent risk or uncertainty in engineering
applications
•Can be interpreted as our degree of belief or 
relative frequency
3-3 Probability
• Probability statements describe the likelihood that 
particular values occur. 
• The likelihood is quantified by assigning a number 
from the interval [0, 1] to the set of values (or a 
percentage from 0 to 100%). 
• Higher numbers indicate that the set of values is 
more likely.
3-3 Probability
• A probability is usually expressed in terms of a 
random variable. 
• For the part length example, X denotes the part 
length and the probability statement can be written 
in either of the following forms
• Both equations state that the probability that the 
random variable X assumes a value in [10.8, 11.2] is
0.25.