5. Probability in our daily lives
Probability = the way uncertainty is quantified
Random phenomena = everyday situations for which the outcome is uncertain
Phenomena = any observable occurrences
5.1. How probability quantifies randomness
Randomness = randomly assigning subjects to treatments / randomly selecting people for a sample /
outcomes to a response variable the possible outcomes are known but it’s uncertain which
outcome will occur for any given observation
With a small number of observations, outcomes of random phenomena may look quite different
from what you expect. Unpredictability for any given observation is the essence of randomness.
With a large number of observations, summary statistics settle down and get increasingly closer to
particular numbers. As we make more observations, the proportion of times that a particular
outcome occurs gets closer and closer to a certain number we would expect. This long-run
proportion provides the basis for the definition of probability
With random phenomena, the proportion of times that something happens is highly random and
variable in the short run, but very predictable in the long run.
Trial = each simulated roll of a die
Cumulative proportion = a running record of the proportion of times a phenomena has occurred, at
each value for the number of trials.
the law of large numbers = as the number of trials increases, the proportion of occurrences of any
given outcome approaches a particular number in the long run. It is assumed that the outcome of
any one trial does not depend on the outcome of any other trial.
We will interpret the probability of an outcome to represent long-run results.
With any random phenomenon, the probability of a particular outcome is the proportion of times
that the outcome would occur in a long run of observations.
Probability is a proportion – so it takes a value between 0 and 1 (or a percentage 0-100)
Different trials of a random phenomenon are independent if the outcome of any one trial is not
affected by the outcome of any other trial.
Like proportions, the total of the probabilities for all the possible outcomes equals 1
Subjective definition of probability = probabilities not based on long-run trials, the probability is
assessed by taking into account all the information that you have (you must rely on subjective rather
than solely objective information)
- The probability of an outcome is defined to be a personal probability – your degree of belief
that something will occurs, based on the available information Bayesian statistics
Probability = the way uncertainty is quantified
Random phenomena = everyday situations for which the outcome is uncertain
Phenomena = any observable occurrences
5.1. How probability quantifies randomness
Randomness = randomly assigning subjects to treatments / randomly selecting people for a sample /
outcomes to a response variable the possible outcomes are known but it’s uncertain which
outcome will occur for any given observation
With a small number of observations, outcomes of random phenomena may look quite different
from what you expect. Unpredictability for any given observation is the essence of randomness.
With a large number of observations, summary statistics settle down and get increasingly closer to
particular numbers. As we make more observations, the proportion of times that a particular
outcome occurs gets closer and closer to a certain number we would expect. This long-run
proportion provides the basis for the definition of probability
With random phenomena, the proportion of times that something happens is highly random and
variable in the short run, but very predictable in the long run.
Trial = each simulated roll of a die
Cumulative proportion = a running record of the proportion of times a phenomena has occurred, at
each value for the number of trials.
the law of large numbers = as the number of trials increases, the proportion of occurrences of any
given outcome approaches a particular number in the long run. It is assumed that the outcome of
any one trial does not depend on the outcome of any other trial.
We will interpret the probability of an outcome to represent long-run results.
With any random phenomenon, the probability of a particular outcome is the proportion of times
that the outcome would occur in a long run of observations.
Probability is a proportion – so it takes a value between 0 and 1 (or a percentage 0-100)
Different trials of a random phenomenon are independent if the outcome of any one trial is not
affected by the outcome of any other trial.
Like proportions, the total of the probabilities for all the possible outcomes equals 1
Subjective definition of probability = probabilities not based on long-run trials, the probability is
assessed by taking into account all the information that you have (you must rely on subjective rather
than solely objective information)
- The probability of an outcome is defined to be a personal probability – your degree of belief
that something will occurs, based on the available information Bayesian statistics
