Quiz 2 Flashcards
What is set theory notation?
“Not” — a^c
“Or” — the union of A and B is the set of all elements that belong to A or B or both. A u B
“And” — the intersection of A and B is the set of all elements that belong to A and B. A n B.
What are the related probability formulas?
P(A) + P(Ac) = 1
P(A u B) = P(A) + P(B) — P(AnB)
P(A n B) + P(A) + P(B) — P(A u B)
What are the deMorgans law?
P(Ac n Bc) = P(A u B)^c = 1 — P(A u B)
P(Ac u Bc) = P(A n B)^c = 1 — P(AnB)
What is the total law of probability?
P(A) = P(A n B) + P(A n Bc)
What is mutual exclusivity?
When there are no element in both A and B
P(A n B) = 0
What is conditional probability?
Is a probability that reflects addictional knowledge that way affect the outcome of an experiment.
P(A|B) = P(AnB) / P(B)
The probiotic of an element belonging to A after restricting our sample space to B
What are discrete random variables?
Variables that can take on countable number of values.
What is a probability distribution tables ?
Appropriate for discrete random variables and is a useful way of displaying all the values a random variable can assume as well as the probabilities associated with all the values
What is the expected value?
E(X) = sum of xipi
The bearings value of x rover a theoretical infinite number of repetitions of an experiment. Measure of central tendency
What is variance of a discrete random variable?
VAR (X) = E(X^2) — (E(X))^2
Measure of spread
is a measure of the variability of X over a theoretical infinite number of repetitions of an experiment
What is standard deviation in a discrete random variable?
SD (X) = squrt (VAR(X))
Measure of variability of X
What is a binomial random variable?
— an experiment consists of a fixed n identical, independent trials
— the experiment involves the same dichotomous (two option) response for each trial
— the probability of “success”, p, remains the same from trial to trial
— the binomial variable itself is defined as the number of successes out of the total n trials
Notations X~bin(n,p)
EX: COIN FLIP (two trials, success or failure, constant trials (p doesn’t change), independent trials)
What is probability mass function (pmf) ?
A probability mass function (pmf) is teh equation that is used to find the probability that a random variable X assumes a particular values x. The following is the pmf for a binomial random variable X
P(X = x) = (n/x)p^x(1-p)^n-x
P(X = x): dbinom(x,n,p)
P(X<x):pbinom(x,n,p)
