probability definition and distribution like normal, binomial and poison

1. Probability

2. Medicine is a science
of uncertainty and an
art of probability.
Probability

3. Latin - Probare meaning to
prove.
Probus – Latin - honest
Probability -Meaning

4. Probability originated
in the problems
dealing with games
of chance

5. Tossing coin

6. Throwing dice

7. Drawing cards

8. In statistics the
term chance is
used as probability.
Probability

9. The relative frequency of
occurrence of an experiment
outcome when repeating the
experiment.
The concept of probability is also used
in biostatistics.

10. Distribution
•Binomial
•Normal
•Poison

11. Binomial distribution
•It is a special type of
Bernouli distribution.
•It is named after

12. Swiss scientist Jacab Bernauli
[ 1654 – 1705 ]
Mathematician
and
Astronomer.

13. When a coin is tossed
outcome is either head or
tail

14. color of eyes of a person
can be either brown or
not brown

15. Answer to a multiple choice
question can be either be correct or
incorrect.
True or False question
Benzene is aliphatic or Aromatic

16. Binomial distribution
Two mutual exclusive
outcome one is success
and other is failure.

17. Binomial distribution
If an experiment is repeated ‘n’ times then the
binomial distribution can be used to determine
the probability of obtaining exactly x success in
the ‘n’ number of trials.

18. • Outcomes are dichotomous-
• Only two outcomes are possible
out of n trial.
• One outcome is termed as
success
• and the other is failure.
Properties of binomial experiment

19. Properties of binomial experiment
• The experiment consist of n repeated
trials.
• The probability of success is same [
constant ] on every trial.
• Trial are independent [ outcome of
one trial does not effect the outcome
of the other.

20. Problem
• Six babies were delivered in the labour ward
of a hospital. Assuming equal probability for
male or female babies.
• A. two male babies.
• B. at least two male babies.

21. Solution
• X is number of male babies.
• P = occurrence of male babies divided by total
occurrence = ½
• There q= 1-p = 1- ½ = ½

22. A.
• P = two male babies x=2
• 6C2 = 6 x 5 = 30/2 = 15
1x 2
= 6 C2 [ ½]2 [1/2]6-2
= 15 x ¼ x 1/16 = 15/64
= 0.234

23. B at least two male babies
• 1- atmost one male baby
• 1- [ f(0) + f (1) ]
• 6C1 = 6/1 =6 6C0 =1
• 1- [ f(0) + f (1) ] = 1- [ 6C0[1/2]0 [1/2]6-0
+
[ 6C1 [1/2]1 [1/2]6-1
= 1- [1 x 1 x 1/64 ] + [ 6 x ½ x 1/32 ]
= 1- [1/64 + 1/64 ] = 1- 7/64 = 57/64= 0.891
= 0.891

24. Events with low
frequency in a large
population follow
poison distribution.
Poison distribution

25. Poison distribution
• It is called as law of small numbers.
• The number of occurrences of an
event that seldom happens but has
many opportunities to happen.
• it takes non negative integer values.

27. • It is unimodal
• It exhibit positive skew that decrease as λ
decreases.
• The variance spread increases as λ decreases.
• Only data required to use poison distribution
is the mean number of occurrence.
• Poison resembles binomial if the probability of
an event is very small.
Poison distribution

28. Application of poison distribution
• It involves counting the number of times a
random event occurs in a given amount of
time.
• Example :
• Number of patients entering the hospital
during a specified time period.

29. Normal or Gaussian distribution
• Central limit theorem
• It states that when a large number of random
variables are independently and identically
distributed with finite variance , their sum is
approximately normally distributed.

30. It is the most important
continuous probability
distribution.
Normal or Gaussian distribution

31. • The behavior of many of the real life
situation can be modeled as normal
distribution.
• Example
• Monthly salary of a employees in a
locality
• Marks of the students in entrance test.
Normal or Gaussian distribution

32. • The data will follow a bell shaped
distribution is called a normal or
Gaussian distribution.
• Data around a central value or the
observation around the mean such a
distribution is called a standard or
normal distribution.
Normal or Gaussian distribution

33. The curve is called normal because
it is the usual distribution of
frequencies in nature when the
number of observation is
extremely large and the class
interval is very small.
Normal or Gaussian distribution

34. • The graph depends on the mean and
standard deviation
• The mean will show the location of
center of the graph
• Standard deviation determines the
height and width of the graph.
Normal or Gaussian distribution