week 1 - Introduction, Randomness & probability

Question 1

outcome

Answer 1

the value of the random phenomenon en we observe it

e.g., heads (or tails)
outcome of H

Question 2

event

Answer 2

a collection of outcomes

e.g., toss 1 = heads & toss 2 = tails

an event of HT

Question 3

sample space

Answer 3

the set of all possible outcomes

e.g., on two tosses {HH, TT, HT, TH}

The probability assignment rule: p(S) = 1
the probability of the whole sample space = 1

Question 4

disjoint

Answer 4

mutually exclusive! (events have no outcomes in common)

knowing “that A” means B cannot occur –

disjoint events CANNOT be independent!

Question 5

random phenomenon

Answer 5

we know what outcomes could happen, but not which particular values will happen

Question 6

Law of Large Numbers

Answer 6

the long-term relative frequency of repeated independent events gets closer to the true frequency as the number of trials increases

seemingly “random” phenomena settle down in a way that is consistent and predictable!

Question 7

independent

Answer 7

learning that one event occurs does not change the probability that the other event occurs

the outcome of one trial doesn’t effect the outcome of the others

Question 8

p

Answer 8

the probability of an event

a number btw 0 and 1 that reports the likelihood of that event’s occurence

For any event A, 0 greater-than or equal to P(A) less-than or equal to 1.

Question 9

empirical probability
vs
theoretical probability
vs
personal probability

Answer 9

the probability attained through long-run relative frequency of the event’s occurence

the probability obtained from a model

subject, personal degree of belief

Question 10

Complement rule

Answer 10

p(A) = 1 - p(Ac)

the probability of the complement of A (the probability that it DOESN’T occur)

Question 11

addition rule

Answer 11

for Disjoint events!
tip-off word: “either” “or”

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

or = U symbol (u for union)!

Question 12

trial

Answer 12

one occasion on which we observe a random phenomenon

e.g., one toss of a coin

Question 13

mutiplication rule

Answer 13

tip-off word: “both”

P(A and B) = P(A) x P(B)

Question 14

“at least one”…

Answer 14

Think about the complement!

What’s the probability you get a red light AT LEAST ONCE during the week?

At least once means 1, 2, 3, 4, or 5 times.
Easier to think about the complement: 0 times
Complement rule, Multiplication rule, then Complement rule again to get the probability of AT LEAST ONCE