IB DP Maths: AI SL复习笔记4.4.1 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)
• 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 that a dice lands on when rolled once
    • this has a finite number of outcomes: {1,2,3,4,5,6}

What is a probability distribution of a discrete random variable?

• 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 discrete probability distribution function or "pdf")
  • They can be represented by vertical line graphs (the possible values for 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?