Question

Please provide
Definitions, some explanation along with example for each topic
(Note: please provide all data in text format pdf/text so i can copy into MsWord because i have to submit my assignment in printed form)

1)Random experiment
2)properties of random experiment
3)sample space
4)event
5)simple event
6)compound event
7)equally likely event
8)mutually exhaustive probability
9)classical or priori probability
10)relative frequency or posterior prob.
11)Axiamatic probability
12) Properties of probability

Answer 1

1)Random experiment :

Random experiment satisfies the following conditions

1)More than one possible result.

2)Its not possible to predict the result in advance

An outcome is a result of a random experiment, the set of all possible outcomes is called Sample space.

Example of random Experiment:

Toss a coin, Sample space S={head, tails}={H,T}

Two coin toss: Sample space S={HH,HT,TT,TH}

Properties of Random Experiment: It performed according to some set of rule, result of each performance depends on chance and cannot be predicated uniquely and it can be repeated arbitrarily often.

Event: The set of outcomes from an random experiment is know as event,

Ex. toss a coin ,The coin landing head or tail these can be said to be the event

Simple Event :its an event where one experiment at a time and it will be having single outcome

Tossing a coin is a simple event

Coumpound Event:

Compound event is the combination of two or more than two simple event ,it can also be deined as an event contains more than one sample points in it .

Ex, tossing a coin twice

Equally likely event :

These are those event which are random and have thus an equal likelihood of occurrences, when the outcomes of an experiment are equally likely to happen, they are called likely events

Consider a coin toss are equally likely to get head or tail.

Mutually exclusive and Exhaustive probability:

Let A and B as a two event and its said to be mutually excusive having P(A or B)=P(A)+P(B)

Event cannot occur together.

A set outcomes is collectively exhaustive if one of the event must occur

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

Classical defination of probability:

It is the ration of number of favourable outcomes and total number of possible outcomes

Properties of probability:

probablity lies between 0 to 1

A is an event then P(A)>=0 ,

Probabiity of impossible event is zero

P(⏀)=0

Axiomatic probability satisfies below three axioms or rule

For an event P(A)>=0

If A and B are mutually exclusive outcomes, P(A ∪ B ) = P(A) + P(B)

S is a sample space then P(S)=1