The presentation discusses probability distributions, explaining that they represent the likelihood of different outcomes for a random variable. It covers three main types: binomial, poisson, and normal distributions, detailing their properties and formulas. Each distribution has unique characteristics, such as the binomial's focus on discrete outcomes and the normal's continuity and symmetry.

1. Presentation on
PROBABILITY
DISTRIBUTION
Mamta Barik
Applied Science Deptt.
*Applied
Mathematics-IV

2. * A probability distribution is a function that describes
the likelihood of obtaining the possible values that a
random variable can assume. In other words, the
values of the variable vary based on the underlying is
probability distribution.
Binomial
Poisson
Normal
They are
of
following
types:

3. 1.BINOMIAL DISTRIBUTION
This distribution is based on Bernoulli’s trials. It is a
discrete distribution. It’s PDF is :
P(x)= nCx px qn-x , 0<x<n
where ,
n is total number of outcomes,
x is possible number of outcomes,
p is probability of success,
q is probability of failure.
Here, p+q=1
Mean=np
Variance=npq

4. * Consider the following question:-

5. 2. POISSON DISTRIBUTION
It is a discrete distribution based on
Bernoulli’s trials. It is a limiting case of binomial
distribution.
When n becomes very large and P becomes very
small then Binomial distribution tends to Poisson
distribution. It’s PDF is:
P(x) = e-λ λ^x / x! ,0<x<∞
* Poisson distribution has the following
properties:-
* Mean of the distribution = λ .
* Variance of the distribution = λ .

6. * Consider the following question:-

7. 3. NORMAL DISTRIBUTION
It is a continuous probability distribution whose
Probability Mass Function(PMF) is:
P(x)= [1/
-∞<x<∞
It’s Mean= μ
Variance= σ2
Standard Deviation= σ
It is a limiting case of Binomial distribution. When n
becomes very large and P becomes close to ½ then
B.D tends to Normal distribution.
σ√2Π]*e[(-1/2)(x-μ/σ)2]

8. 3. NORMAL DISTRIBUTION
It is a symmetrical distribution. In this, we convert x
into z by the transformation:
z= (x-μ)/σ
Total area under the normal curve is unity.
P(-∞<z<∞)= 1
P(-∞<z<0)=P(0<z<∞)= 0.5
-∞ z=0 ∞

9. * Consider the following question:-

10. THANK YOU!