5: Concepts and Applications in Probability

Question 1

correlation is _____ causation

Answer 1

NOT

Question 2

reverse causation

Answer 2

does x cause y or y cause x

Question 3

common response

Answer 3

observed association b/w X and Y is actually caused by lurking variable Z. Both X and Y change in response to changes in Z

Question 4

confounding

Answer 4

both X and Z may influence Y

because X is confounded with Z, we cannot distinguish the influence of X from the influence of Z. thus, we can’t say how strong the direct effect of X on Y is

Question 5

sample space

Answer 5

set of all possible outcomes

Question 6

event

Answer 6

outcome or set of outcomes of a random phenomenon (no boys, no girls, one boy etc)

Question 7

P(A)

Answer 7

of outcomes in Event A (freq A) / total number of outcomes in sample space S

Question 8

complement rule

Answer 8

for any event A, P(A^c) = 1 - P(A)

Question 9

addition rule for disjoint (mutually exclusive events)

Answer 9

P(A or B) = P(A) + P(B)

Question 10

General Addition Rule (Events A and B are NOT disjoint)

Answer 10

P(A or B) = P(A) + P(B) - P(A and B)

Question 11

Conditional Probability

Answer 11

probability of event A occurring GIVEN THAT Event B has occurred.

P(A|B) = P(A and B) / P(B)

(A and B are disjoint/mutually exclusive)

Question 12

Joint Probability, General Formula for 2 Dependent Events

Answer 12

P(A and B) - probability that both A and B occur together.

P(A|B) = P(A and B) / P(B)
–> P(A and B) = P(B)* P(A|B)

Question 13

Joint Probability, Multiplication Rule for Independent Events

Answer 13

P(A and B) = P(A)*P(B) if and only if A and B are independent

Question 14

random variable

Answer 14

variable whose numerical values are determined by the outcome of a random phenomenon

Question 15

discrete random variable X

Answer 15

X assumes a numerical value for each outcome of the sample space.

Question 16

continuous random variable X

Answer 16

can take any value in an interval of numbers. probability distribution of a continuous random variable X is described by a density curve. probability model for a continuous random variable assigns probabilities to intervals of outcomes (rather than individual outcomes).

Question 17

normal probability distribution

Answer 17

theoretical distribution of a continuous random variable, shows what values the random variable can take and is used to assign probabilities to intervals based on those values