What is a random variable?
A variable whose values describe the outcome of an experiment
What is a discrete random variable?
A variable that takes on a list of values that are finite in size
What is a continuous random variable?
A variable that can take on any value over an interval (uncountable: infinite possible values)
What makes a variable discrete?
If the variable exists within set bounds (it is countable)
How can a variable be discrete, countable but also infinite?
EX: Tossing a coin infinitely
Let X = # Tails before heads
-> Discrete because the values are still countable, but infinite because the streak of tails can go on forever in theory
Example of a discrete finite variable
Rolling a die two times.
- Set number of outcomes (ranging from 2 to 12)
Examples of continuous variables
1) Weight in Kg: Can have any level of accuracy, therefore infinite possible values
2) WiFi download speed: Infinite possible decimals
What is a discrete probability distribution?
What are the criteria?
A function or table that assigns probabilities to the outcomes of a discrete random variable
1) P(x) >= 0 for all X (no outcomes can have a probability of 0)
2) ∑ P(x) = 1 (The probabilities must add up to one)
What is a binomial experiment?
(4 characteristics)
1) Consists of n independent AND identical trials
2) Two outcomes per trial (success or failure)
3) The probability of success, P, never changes between trials
4) The probability of failure is q where p +q = 1
Example: a coin toss (assigning success and failure to each side)
What is the expectation value?
What kind of variable does it apply?
The mean of a probability distribution.
Only applies to discrete random variables.
