Discrete Random Variables

Random variables, assigning probabilities to all outcomes, binomial distribution, probability mass function vs cumulative probability function

What is a random variable?

Set of values that quantify the outcome of the random experiment 

• Allows you to map the outcomes of a random experiment to numbers 

• Usually denoted with a capital letter 

What is a discrete random variable?

Can assume only a finite number of different values 

• E.g. outcome of a coin toss 

What are the assumptions of discrete random variable experiments?

• All outcomes are equally likely

• All outcomes are independent from each other

What is a continuous random variable?

Arbitrarily precise → can take all values in some range 

• E.g. height 

What are probability distributions used for?

Mapping the values of a random variable to the probability of it occurring

How can discrete probability distributions be plotted?

On a bar graph

What are probability mass functions used for?

Giving the probability that a discrete random variable exactly equals a specific value

What is the equation for when you have a random experiment with N possible outcomes?

What is the equation for any subset A of the sample space?

What are frequency distributions used for?

Mapping the values of a random variable with how often they occur

What is binomial distribution?

• Type of discrete probability distribution 

• Only 2 possible outcomes: success + failure

• Number of observations (n) is fixed 

• Each observation is independent of each other 

• Probability of success (p) is the same for each observation 

• Number of successes given a fixed number of trials 

What is the equation for binomial probability mass function?

What is the code for calculating binomial probability mass functions?

What are cumulative distribution functions used for? How does this relate to binomial distribution?

Seeing the total probability of all values before or after a given point → with BD the CPF simply sums the probabilities of the individual outcomes 

What is the code for calculating cumulative probabilities?

Interpreting cumulative distribution frequencies