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??