Project by Ms.Mamta Barik Assistant Professor of JIMS management Technical Campus,Greater Noida. A probability distribution is a function that portrays the probability of acquiring the potential qualities that an irregular variable can assume. In other words the estimations of the variable fluctuate dependent on the hidden probability distribution.

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!