# MATH 109 Lecture Notes - Lecture 6: Submarine Sandwich

6.1

●Probability model: a description of how a statistician thinks data are produce.

○When the word model

to remind that our description does not really explain how the

data came into existence.

○Example: if a model says that the probability of getting heads when we flip a coin is 0.54,

but in fact we get heads 50% of the time, we suspect that the model is not a good

match.

●Probability distribution (Probability Distribution Function; pdf): a tool that helps us by keeping

track of the outcomes of a random experiment and the probabilities associated with those

outcomes.

○Example: a playlist that has 10 songs: 6 are Rock, 2 are Country, 1 HipHop, and 1 Opera.

Put the playlist on shuffle.

Outcome

Probability

Rock

6/10

Non-Rock

4/10

KEYPOINT: A probability distribution tells us (1) all the possible outcomes of a random experiment,

and (2) the probability of each outcome.

●Discrete Outcomes (or discrete variables): numerical values that you can list or count.

○Example: the number of phone numbers stored on the phones of your classmates.

●Continuous Outcomes (or continuous variables): cannot be listed or counted because they

occur over a range.

○Example: the length of your next phone call will last a continuous variable.

Example 1: Discrete or Continuous

Consider these variables:

A. The weight of a submarine sandwich you’re served at a deli. Continuous

B. The elapsed time from when you left your house to when you arrived in class this morning.

Continuous

C. The number of people in the next passing car. Discrete

D. The blood-alcohol level of a driver pulled over by the police in a random sobriety check.

(Blood-alcohol level is measured as the percent of the blood that is alcohol). Continuous

E. The number of eggs laid by a randomly selected salmon as observed in a fishery. Discrete

Discrete Probability Distributions Can Be Tables or Graphs

## Document Summary

Probability model : a description of how a statistician thinks data are produce. When the word model to remind that our description does not really explain how the. Probability distribution (probability distribution function; pdf) : a tool that helps us by keeping track of the outcomes of a random experiment and the probabilities associated with those outcomes. Example : a playlist that has 10 songs: 6 are rock, 2 are country, 1 hiphop, and 1 opera. Keypoint : a probability distribution tells us (1) all the possible outcomes of a random experiment, and (2) the probability of each outcome. Discrete outcomes (or discrete variables) : numerical values that you can list or count. Example : the number of phone numbers stored on the phones of your classmates. Continuous outcomes (or continuous variables) : cannot be listed or counted because they occur over a range. Example : the length of your next phone call will last a continuous variable.