Discrete Random Variables
Mathematical Modelling 2
Week 3: Discrete Random Variables
Stephen Bush Department of Mathematical Sciences
MM2: Statistics
- Week 3 -
1
Random Variables
• Reference: Devore § 3.1 – 3.5 • Definitions:
• An experiment is any process of obtaining one outcome where the outcome is uncertain. • A random variable is a numerical variable whose value can change from one replicate of the experiment to another.
• Sample means and sample standard deviations are random variables
• They are different from sample to sample. • Population means and standard deviations are not random.
MM2: Statistics - Week 3 2
Random Variables - Examples
• Experiment 1: Pick a student at random from the class
• Let X denote the height of the student
• Experiment 2: Throw a fair dice
• Let X denote the outcome of the dice. X = 1,2,3,4,5, or 6.
• Notice that the outcome of both of these events changes every time you take a new sample.
MM2: Statistics
- Week 3 -
3
1
Random Variables
• A random variable can be continuous or discrete.
• Continuous random variables can take any real value, such as measurements. • Electrical current, length, pressure, temperature, time voltage, weight etc. • Discrete random variables are usually counts (whole numbers). • Number of scratches on a surface, proportion of defective parts among 1000 tested, number of transmitted bits received in error, number of vehicles on a bridge. • The methods that we use to analyse these random variables differ between continuous and discrete.
• Experiment 1 (Height): Continuous • Experiment 2 (Roll of Dice): Discrete
MM2: Statistics - Week 3 4
Random Variables
• Decide whether a continuous or a discrete random variable is the best model for each of the following variables.
• The life time of a biomedical device after implant in a patient. • The number of times a transistor in a computer memory changes state in one operation. • The strength of a concrete specimen. • The number
Week 3: Discrete Random Variables
Stephen Bush Department of Mathematical Sciences
MM2: Statistics
- Week 3 -
1
Random Variables
• Reference: Devore § 3.1 – 3.5 • Definitions:
• An experiment is any process of obtaining one outcome where the outcome is uncertain. • A random variable is a numerical variable whose value can change from one replicate of the experiment to another.
• Sample means and sample standard deviations are random variables
• They are different from sample to sample. • Population means and standard deviations are not random.
MM2: Statistics - Week 3 2
Random Variables - Examples
• Experiment 1: Pick a student at random from the class
• Let X denote the height of the student
• Experiment 2: Throw a fair dice
• Let X denote the outcome of the dice. X = 1,2,3,4,5, or 6.
• Notice that the outcome of both of these events changes every time you take a new sample.
MM2: Statistics
- Week 3 -
3
1
Random Variables
• A random variable can be continuous or discrete.
• Continuous random variables can take any real value, such as measurements. • Electrical current, length, pressure, temperature, time voltage, weight etc. • Discrete random variables are usually counts (whole numbers). • Number of scratches on a surface, proportion of defective parts among 1000 tested, number of transmitted bits received in error, number of vehicles on a bridge. • The methods that we use to analyse these random variables differ between continuous and discrete.
• Experiment 1 (Height): Continuous • Experiment 2 (Roll of Dice): Discrete
MM2: Statistics - Week 3 4
Random Variables
• Decide whether a continuous or a discrete random variable is the best model for each of the following variables.
• The life time of a biomedical device after implant in a patient. • The number of times a transistor in a computer memory changes state in one operation. • The strength of a concrete specimen. • The number