Basic Basics of Statistics(Descriptive) & Probability for Data Scientists-A Quick Refresher
Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.
In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned. If
E represents an event, then
P(E) represents the probability that
Ewill occur. A situation where
E might happen (success) or might not happen (failure) is called a trial.
This event can be anything like tossing a coin, rolling a die or pulling a colored ball out of a bag. In these examples the outcome of the event is random, so the variable that represents the outcome of these events is called a random variable.
The empirical probability of an event is given by number of times the event occurs divided by the total number of incidents observed. If for
ntrials and we observe
ssuccesses, the probability of success is s/n.
Theoretical probability on the other hand is given by the number of ways the particular event can occur divided by the total number of possible outcomes.
JOINT AND CONDITIONAL PROBABILITY
Joint Probability: Probability of events A and B denoted by
P(A and B) or P(A ∩ B)is the probability that events A and B both occur.
P(A ∩ B) = P(A). P(B) . This only applies if
Bare independent, which means that if
Aoccurred, that doesn’t change the probability of
B, and vice versa.
Conditional Probability: When A and B are not independent, it is useful to compute the conditional probability, P (A|B), which is the probability of A given that B occurred:
P(A|B) = P(A ∩ B)/ P(B).
The probability of an event A conditioned on an event B is denoted and defined
P(A|B) = P(A∩B)/P(B)
P(B|A) = P(A ∩ B)/ P(A) . We can write the joint probability of as A and B as
P(A ∩ B)= p(A).P(B|A), which means : “The chance of both things happening is the chance that the first one happens, and then the second one given the first happened.”