probability distribution.pptxprobability distribution.pptxprobability distribution.pptx

1. Probability
Distribution

2. Theoretical Distribution
A random exponent is assumed as a model for theoretical distribution,
and the probabilities are given by a function of the random variable is
called probability function.
For example, if we toss a fair coin, the probability of getting a head is
12. If we toss it for 50 times, the probability of getting a head is 25. We
call this as the theoretical or expected frequency of the heads. But
actually, by tossing a coin, we may get 25, 30 or 35 heads which we
call as the observed frequency.
Thus, the observed frequency and the expected frequency may equal
or may differ from each other due to fluctuation in the experiment.

3. Types of Theoretical Distribution
 Binomial Distribution
 Poisson distribution
 Normal distribution or Expected Frequency distribution

4. Binomial Distribution:
The prefix ‘Bi’ means two or twice. A binomial distribution can be
understood as the probability of a trail with two and only two
outcomes. It is a type of distribution that has two different outcomes
namely, ‘success’ and ‘failure’. Also, it is applicable to discrete random
variables only.
Thus, the binomial distribution summarized the number of trials, survey
or experiment conducted. It is very useful when each outcome has an
equal chance of attaining a particular value. The binomial distribution
has some assumptions which show that there is only one outcome and
this outcome has an equal chance of occurrence.

5. The number of the trial or the experiment must be fixed.Every trial is
independent. None of your trials should affect the possibility of the next
trial.
The probability always stays the same and equal. The probability of
success may be equal for more than one trial.

6. Poisson Distribution :
The Poisson Distribution is a theoretical discrete probability distribution
that is very useful in situations where the events occur in a continuous
manner. Poisson Distribution is utilized to determine the probability of
exactly x0 number of successes taking place in unit time. Let us now
discuss the Poisson Model.
At first, we divide the time into n number of small intervals, such that n
→ ∞ and p denote the probability of success, as we have already
divided the time into infinitely small intervals so p → 0. So the result must
be that in that condition is n x p = λ (a finite constant).

7. Normal Distribution :
The Normal Distribution defines a probability density function f(x) for the
continuous random variable X considered in the system. The random
variables which follow the normal distribution are ones whose values can
assume any known value in a given range.
We can hence extend the range to – ∞ to + ∞ . Continuous Variables
are such random variables and thus, the Normal Distribution gives you
the probability of your value being in a particular range for a given trial.
The normal distribution is very important in the statistical analysis due to
the central limit theorem.
The theorem states that any distribution becomes normally distributed
when the number of variables is sufficiently large. For instance, the
binomial distribution tends to change into the normal distribution with
mean and variance.