Probability’s definition

Probability

is the chance that something will occur though it is that events will occur.

Often you can calculate probability of a number like “15% chance”, or

you can use expressions like impossible, unlikely, and possible, even chance,

likely and certain.

Mathematics

has many branches one of them is probability which is expressed as a number

between 0 and 1, and that’s measured by that kind given by the occurrence of real

event.

For

example the probability of coin toss has only two options either ‘’tails’’ or

‘’heads’’ this case is considered a probability of one.

Probability

of 0.5 is believed to include similar odds if happening or not happening such

as the probability of a coin toss resulting ‘’heads’’ or ‘’tails’’ but for the

probability of zero is believed to be impossibility, in this case the coin will

land flat without either side facing up that is zero that’s the reason ‘’head’’

or ‘’tails’’ must be facing up

It’s

the easiest way can be mathematically

considered as the number of occurrence of specific event divided by the

number of occurrence added to the number of failures of occurrence . Pa=Pa/ (Pa+Pb)

On

throwing a single die , there’s six possibilities :1,2,3,4,5,6

The

probability of one of them 1/6

Probability

theorems:

Bapat-beg

theorem : In probability theory, the Bapat–Beg theorem provides the joint

probability distribution of order statistics of independent

All components of the sample gained from the same population and thus

have the same probability

distribution, and the

Bapat–Beg theorem shows the order statistics when each component of the sample gained

from a various statistical population and therefore it has its own probability

distribution.

Markov-krein theorem:

It states that the predicted values of real function of

random variables where only the early moments of random variable are known.

Craps principle theorem:

it’s the theory which talks about event

probabilities below Independent

and identically distributed random variables

trails , as E1 and E2 gives two mutually exclusive events which may happen on a

given trial.

Types of random

variables:

A Random Variable is a set of considerable significances from a random experiment.

There are two types of random

variables:

1-Discrete random variable:

It has limited available significances

or an unlimited series of certain numbers

– X: number of hits on trying 20 free throws.

2-

Continuous random variable:

It

takes all uncountable values in a period of real numbers

– X: the period it

takes for a lamp to burn.

Types

of probability distributions:

1-Geometric

distribution:

On independent Bernoulli trials are

made over and over, and each with probability (p) of success, the number of

trials (X), and it takes to get the first success has a geometric distribution.

2-Negative

binomial distribution:

Each with probability (P) of

success, and (X) is the trial number when (r) successes are first accomplished,

then X has a non-positive binomial distribution. PS: that Geometric (p) =

Negative Binomial (p, 1).

References:

o

https://mathcs.clarku.edu/~djoyce/ma218/distributions.pdf

o

http://www.stat.purdue.edu/~xuanyaoh/stat350/xyFeb6Lec9.pdf

o

https://link.springer.com/chapter/10.1007/978-1-4612-4638-1_6

o

http://www.mathsisfun.com/definitions/probability.html