2. Probability Distribution
• Listing of all possible outcomes of an experiment
together with their probabilities
• Ex Toss of fair coin 2 times
OUTCOME PROBABILITY
TT ¼
TH ¼
HT ¼
HH ¼
What is Probability Distribution of number of heads
4. Random Variable
• Random variable is a real number ‘x’
associated with the outcome of a random
experiment
• Random Variable ‘x ‘ is of 2 types
- Discrete Random Variable
- Continuous Random Variable
5. Discrete & Continuous Random
Variable
• Discrete Random Variable – ‘x’ can take values
which are countable and can be denoted as a
‘number ‘ .
‘x’ is 0,1,2,3,4………..
ex number of defectives in sample of ‘k’ items
• Continuous Random Variable – ‘x’ can take any
values between 2 given numbers and can have
infinite number of possible values in that range
ex possible weights , heights , temperature ,
distance in a given interval
6. Discrete Probability Distribution
• A discrete random variable assumes each of
its values with a certain “probability”
• A table listing all possible values that discrete
random variable can take along with
associated probabilities is called “ Discrete
Probability Distribution”
7. Types of Discrete Probability
Distribution
Two types
• Binomial Distribution
• Poisson Distribution
10. Binomial Distribution
• Experiments with only 2 outcomes are
“Binomial Experiments "and the two
outcomes are called ‘success (p)’ and ‘failure
(q)’
ex toss of a coin, throw of dice – either even
or odd number will come , either vote for a
candidate or don’t vote for that candidate
11. Binomial Distribution
1 . If one outcome appears , the other cannot appear – two outcomes
are ‘mutually exclusive’
2.Since there is no other possibility, these two outcomes are
‘collectively exhaustive’
3. Since two outcomes are ‘mutually exclusive’ and ‘exhaustive’ , the
sum of their individual probabilities is equal to 1
p+ q=1
p= probability of success
q=probability of failure
Probability distribution of success is called ‘Binomial Distribution”
12. Assumptions in Binomial Experiments
• Process in which each trial (experiment) can
result in one of 2 states is called “Bernoulli or
Binomial Process”
1 .Each trial has 2 possible outcomes called
‘success ‘ and ‘failure’
2.There is finite number of trials ‘n’
3.All trials are identical i.e. probability of each
trial is same
4.Trials are independent of each other
21. Problem
• If a new drug is found to be effective 40% of
the time , then what is the probability that in
a random sample of 4 patients , it will be
effective on 2 of them
