This document discusses different types of continuous probability distributions including uniform, normal, and exponential distributions. It provides examples of how each distribution is used and defined mathematically. The normal distribution is described as the most important for describing continuous random variables. Real-world examples of when each distribution would be used are given, such as height, test scores, and time between events. Business applications like risk evaluation, sales forecasting, and manufacturing costs are also summarized. Finally, it emphasizes that probability is involved in many aspects of daily life beyond just academics.

1. A Presentation By, Sourav Snai,
Debjit Das,
Amrita Nandi,
Arpita Acharjya

2.  Continuous probability distribution is a
probability in which a random variable X
can be taken on any values (continuous)
because there are infinite values that X
could assume, the probability of X taking
on any one specific values is zero.
Therefore we often take ranges of values.

3. Any variable can have two types of values.
Either the values can be fixed number
which is also known as discrete values or
a specified range that is known as
continuous values

4.  The probability that a continuous
variable will take a specific value is zero.
 Because of this we can never express
continuous probability in tabular form it
is always expressed in a equation form or
a formula to describe such kind of
distribution.

5.  A continuous random variable say Y is
following uniform distribution such that
the probability between 4 and 9 is ‘r’.
Find the value of r.
Solution-
In a uniform distribution, the probability is
same for all possible values of a given
variable between the specified range so if
P is the probability of any value between

6. Say a and b ten P=
1
--------------
(b – a)
Since the sum of all probability is 1 .
Here P=r, a=4 and b=9

7.  So
1
r = _______________
( 9 – 4 )
1
= _____
5

8.  Uniform probability.
 Normal probability.
 Exponential probability.

9.  the normal probability distribution is the
most important distribution for
describing a continuous random variable.
 It is used for finding
- height of the people.
- scientific measurement.
- test scores.
- amount of rain fall.

10.  Normal Probability Density Function
 μ = mean
 σ = standard deviation
 Л = 3.14159
 ℮ = 2.71828
2
)(
2
1
2
1
)( 





x
exf

12.  The highest point on the normal curve is
the mean, which is also the median and
the mode.

13.  The mean can be any numerical value:
negative or positive.
 The standard deviation determines the
width of the curve. Larger values result
in wider, flatter curves.
 Probability for the normal variable are
given by the areas under the curve. The
total area under the curve is 1

14. .5 to the left of the mean and .5 to the right.

15.  The uniform probability is perhaps the
simplest distribution for a continuous random
variable.
 This is a rectangular in shape and is defined by
minimum and maximum values.

21.  Used to measure the time that elapses between
two occurrences of an event (the time between
arrivals)
 Examples:
 Time between trucks arriving at an
unloading dock
 Time between transactions at an ATM
Machine
 Time between phone calls to the main
operator

22.  The probability that an arrival time is equal to
or less than some specified time a is
P(0 ≤ x ≤ a) = 1- e^-λa
Where 1/λ is the mean time between events.
Note that if the number of occurrences per
time period is Poisson with mean , then the
time between occurrences is exponential with
mean time 1/ 

23.  Shape the exponential distribution.

24. Example: Customers arrive at the claims counter at
the rate of 15 per hour. What is the probability that
the arrival time between consecutive customers is
less than five minutes?
 Time between arrivals is exponentially distributed with
mean time between arrivals of 4 minutes (15 per 60
minutes, on average)
 1/ = 4.0, so  = .25
 P(x < 5) = 1 - e-a = 1 – e-(.25)(5) = .7135

25.  Scenario analysis.
- worst case
- best case
The worst case would contain some values
from the lower end of the probability,
likely form the middle and the best case
would contain upper end values.

26. Risk evaluation.
determines the chances of loss or profit
earned in the business organization.
Sales forecasting.
it helps to determine the sales quantity of
a product in a particular term(year,
quarter, month).

27. Probability in manufacturing.
it can help to determine the cost benefit
ratio or the transfer of a new
manufacturing technology process by
addressing the likelihood of improved
profit.

28.  From the above we can see that all the three
distribution has application in business but the
most important of all being normal
distribution. It is extensively used in statistical
decision making. It can be transformed to the
corresponding standard normal distribution
which can be used to find probability
associated with the origin normal distribution.
We could also see how it is used to find the
profit and loss chances in a business.

29. Even in our day to day life probability is involved
i.e. - the probability of attending math class by
students on a Monday after a nice holiday of
two days. If we think really carefully it is
involved in every aspect of our life. Even
during birth of a baby the probability of a boy
being born is ½ and a girl is ½ since either a
boy or girl can be born therefore P = 1.
probability is just not a book subject it can be
applied in every situation in our life.

30. Adamas University
References: www.slideshare.com
www.google.com/wikipedia/
Nav Kumar Sir’s Notes