CIE A Level Maths: Probability & Statistics 1复习笔记3.1.1 Discrete Probability Distributions

What is a discrete random variable?

• A random variable is a variable whose value depends on the outcome of a random event
  • The value of the random variable is not known until the event is carried out (this is what is meant by 'random' in this case)
• Random variables are denoted using upper case letters (X , Y , etc )
• Particular outcomes of the event are denoted using lower case letters ( x, y, etc)
• A discrete random variable (often abbreviated to DRV) can only take certain values within a set
  • Discrete random variables usually count something
  • Discrete random variables usually can only take a finite number of values but it is possible that it can take an infinite number of values (see the examples below)
• Examples of discrete random variables include:
  • The number of times a coin lands on heads when flipped 20 times
    (this has a finite number of outcomes: 0,1,2,…,20)
  • The number of emails a manager receives within an hour
    (this has an infinite number of outcomes: 1,2,3,…)
  • The number of times a dice is rolled until it lands on a 6
    (this has an infinite number of outcomes: 1,2,3,…)
  • The number on a bingo ball when one is drawn at random
    (this has a finite number of outcomes: 1,2,3…,90)

What is a probability distribution?

• A discrete probability distribution fully describes all the values that a discrete random variable can take along with their associated probabilities
  • This can be given in a table
  • Or it can be given as a function (called a probability mass function)
  • They can be represented by vertical line graphs (the possible values for X  along the horizontal axis and the probability on the vertical axis)
• The sum of the probabilities of all the values of a discrete random variable is 1

How do I calculate probabilities using a discrete probability distribution?

• First draw a table to represent the probability distribution
  • If it is given as a function then find each probability
  • If any probabilities are unknown then use algebra to represent them

How do I know which inequality to use?