Basic Concepts of Probability Approaches to Probability Bayes' Theorem Binominal Distribution Poisson Distribution Normal Distribution

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Basic Concepts of Probability
Approaches to Probability
Bayes’ Theorem
Binomial Distribution
Poisson Distribution
Normal Distribution
Lecture # 2

3. We may come across the statements like:
the train may come late today,
the chance of winning the cricket match etc.
It means there is uncertainty about the happening of the
event(s).
We live in a world where we are unable to forecast the future
with complete certainty. Our need to cope with uncertainty
leads us to the study and use of probability.
Probability

4. Formula of
Probability

5. The probability theory was first applied to gambling and later
to other socio-economic problems.
The probability theory was later on applied to the insurance
industry, which evolved in the 19th century to estimates
of the life expectancy of the insurance policy holder.
Consequently, the study of probability was initiated at many
learning centers for students to be equipped with a tool
for better understanding of many socio-economic
phenomenon.
Lately, the quantitative analysis has become the backbone of
statistical application in business decision making and
research.
Probability
History

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It is a way of finding a
probability when we know other
probabilities

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16. There are two types of Probability
Distribution;
1) Discrete Probability
Distribution- the set of all
possible values is at most a
finite or a countable infinite
number of possible values
2) Continuous Probability
Distribution- takes on values
at every point over a given
interval
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Discrete
Probability
Poisson
Distribution
Binomial
Distribution
Continuous
Probability
Normal
Distribution

17. It is defined as a continuous frequency
distribution of infinite range (can take any values
not just integers as in the case of binomial and
Poisson distribution).
The normal distribution was first discovered by
Abraham de Moivre, a French mathematician he
published an article on Doctrine of Chances in
1733.
Later it was applied in natural and social science
by Laplace in 1777.
The Normal Distribution is also known as
Gaussian distribution in honor of Karl Friedrich
Gauss in 1809.

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The percentage of values in
some commonly used intervals
are:
 68.3% of the values of a
Normal random variable are
within plus or minus ± one
SD of its mean
 95.4% of the values of a
Normal random variable are
within plus or minus ± two SD
of its mean
 99.7% of the values of a
Normal random variable are
within plus or minus ± three
SD of its mean

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21. The binomial distribution is the discrete
probability distribution that gives only two
possible results in an experiment,
either Success or Failure.
Binomial distribution is applicable for a
random experiment comprising a finite
number (n) of independent Bernoulli trials
having the constant probability of success
for each trial.

22. Binomial Distribution was discovered by
J. Bernoulli (1654-1705) and was first
published eight years after his death
i.e. in 1713 and is also known as
“Bernoulli distribution for n trials”.
Who
Discovered
It

24. ● There are two possible outcomes: true or false, success or failure, yes or no.
● There is ‘n’ number of independent trials or a fixed number of n times
repeated trials.
● The probability of success or failure varies for each trial.
● Only the number of success is calculated out of n independent trials.
● Every trial is an independent trial, which means the outcome of one trial
does not affect the outcome of another trial.
● The terms p and q remain constant throughout the experiment
○ p is the probability of a success on any one trial
○ q = (1-p) is the probability of a failure on any one trial
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25. mathematician proposed
Poisson Distribution.
It is a that expresses the
probability of a given number of events occurring
in a fixed interval of time or space if these events
occur with a known constant rate
and of the time since the last event.
Poisson distribution is used to estimate how many
times an event is likely to occur within the given
period of time.
Poisson
Distribution

26. 1. Each success must be independent of any other
successes.
2. The Poisson random variable, X, counts the number of
successes in the given interval.
3. The mean number of successes in a given interval must
remain constant.
4. For a Poisson distribution, the mean and variance are
given by where λ is the mean number of successes in a
given interval.
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