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?(similar to GCSE)
  • Or it can be given as a?function?(called a probability mass function)
  • 

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 themIdentify which values of the random variable satisfy the inequality or event in the brackets
• • Add together the corresponding probabilities

How do I know which inequality to use?