Quiz 2

Question 1

What is set theory notation?

Answer 1

“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.

Question 2

What are the related probability formulas?

Answer 2

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)

Question 3

What are the deMorgans law?

Answer 3

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)

Question 4

What is the total law of probability?

Answer 4

P(A) = P(A n B) + P(A n Bc)

Question 5

What is mutual exclusivity?

Answer 5

When there are no element in both A and B

P(A n B) = 0

Question 6

What is conditional probability?

Answer 6

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

Question 7

What are discrete random variables?

Answer 7

Variables that can take on countable number of values.

Question 8

What is a probability distribution tables ?

Answer 8

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

Question 9

What is the expected value?

Answer 9

E(X) = sum of xipi

The bearings value of x rover a theoretical infinite number of repetitions of an experiment. Measure of central tendency

Question 10

What is variance of a discrete random variable?

Answer 10

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

Question 11

What is standard deviation in a discrete random variable?

Answer 11

SD (X) = squrt (VAR(X))

Measure of variability of X

Question 12

What is a binomial random variable?

Answer 12

— 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)

Question 13

What is probability mass function (pmf) ?

Answer 13

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)