Lecture 5

Question 1

experiment

Answer 1

act or process of observation that leads to a single outcome that cannot be predicted with certainty

Question 2

sample point

Answer 2

most basic outcome of an experiment

Question 3

sample space (universal set)

Answer 3

collection of all the experimental elements

Question 4

probability rules

Answer 4

let xi, i=1,2,3….k, denote a possible outcome for the random variable X, and let P(X=xi)=pi denote the probability of that outcome. Then: 0< P(xi)<1 and the sum of all of probabilities =1 (each probability falls between 0 and 1 inclusive and the total probability must equal 1

Question 5

event

Answer 5

is a specific collection of sample points

Question 6

probability of an event

Answer 6

calculated by summing the probabilities of the sample points in the sample space for A

Question 7

Steps for calculating probabilities of events

Answer 7

1. define the experiment; describe the process used to make an observation and type of observation that will be recorded
2. List the sample points
3. Assign probabilities to the sample points
4. determine the collection of sample points contained in the event of interest
5. sum the sample point probabilities to get the probability of the event

Question 8

combination rule

Answer 8

a sample of n elements is to be drawn from a set of N elements. Then, the number of different samples possible is denoted by (N n) and is equal to: N!/(n!)(N-n)!
where the factorial symbol ! means that n!= (1)(2)(3)…(n-1)(n)

Question 9

union of two events A and B

Answer 9

the union of two events A and B, denoted by A U B, is the set of all elements that are in A OR in B OR in both

Question 10

Intersection of two events A and B

Answer 10

the intersection, denoted by A (backwards U) B, is the set of all elements that are in A AND in B

Question 11

complement

Answer 11

when the event does NOT occur- that is, the event consisting of all sample points that are not in the event. We denote the complement of A by Ac.

Question 12

rule of complements

Answer 12

the sum of the probabilities of complementary events equals 1; P(A) +P(Ac)=1

Question 13

additive rule of probability

Answer 13

the probability of the union of events A and B is the sum of the probability of event A and the probability of event B minus the probability of the intersection of events A and B; P(AUB)=P(A) +P(B) -P( A backwards U B)

Question 14

mutually exclusive events

Answer 14

two events A and B are said to be mutually exclusive events if A backwards U B contains no sample points, that is A and B have no sample points in common

Question 15

probability of two mutually exclusive events

Answer 15

if two events A and B are said to be mutually exclusive then, P(AUB)= P(A) + P(B) ( P(A backwards U B) =0)