1. Chapter 1 ІМќ Discrete Probability Distribution: Binomial Distribution
INSTITUT MATEMATIK
K E J U R U T E R A A N
U N I M A P

2. Binomial Distribution
Binomial distribution is the probability distribution of the number of successes in n trials.
E.g.
No. of getting a head in tossing a coin 10 times.
No. of getting a six in tossing 7 dice.
No of missile hits the target.
Lecture 4
Abdull Halim Abdul

3. Binomial distribution is characterised by the number of trial, n and
the probability of success in each trial, p
And is denoted by B(n,p)
Lecture 4
Abdull Halim Abdul

4. If a random variable X is distributed binomial with the parameter n and p then
X ~ B(n,p)
The probability distribution of X is
P(X=x) = nCxpx(1-p)n-x
*Page 221 (text book)
*in text book π is used instead of p
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Abdull Halim Abdul

5. Example If X~B(4,0.1) then P(X=3) = 4C3(0.1)3(0.9)1 = 0.0036
P(X≥4) = P(X=3)+P(X=4) =
What if n is large? Calculation would be tedious. Solution… using cummulative binomial distribution table or statistical software or excel spreadsheet.
Lecture 4
Abdull Halim Abdul

6. Using excel will be discussed using a few examples.
cummulative binomial distribution table already discussed at school. It will only be discussed in the tutorial.
Using excel will be discussed using a few examples.
Lecture 4
Abdull Halim Abdul

7. Poisson Distribution
Poisson distribution is the probability distribution of the number of successes in a given space*.
*space can be dimensions, place or time or combination of them
E.g.
No. of cars passing a toll booth in one hour.
No. defects in a square meter of fabric
No. of network error experienced in a day.
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Abdull Halim Abdul

8. Poisson distribution is characterised by the mean success, λ.
And is denoted by Po(λ)
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Abdull Halim Abdul

9. If a random variable X is distributed Poisson with the parameter λ then
X ~ Po(λ)
The probability distribution of X is
*Page 228 (text book)
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Abdull Halim Abdul

10. Example If X~ Po(3) then P(X=2) = = 0.2240
P(X>2) = P(X=3)+P(X=4)+…+P(X=∞)
= 1 – [P(X=0)+P(X=1)+P(X=2)] =
To avoid tedious calculation it is easier to use cummulative Poisson distribution table or statistical software or excel spreadsheet.
Lecture 4
Abdull Halim Abdul

11. Using excel will be discussed using a few examples.
cummulative binomial distribution table already discussed at school. It will only be discussed in the tutorial.
Using excel will be discussed using a few examples.
Lecture 4
Abdull Halim Abdul

12. Why Normal Distribution
Numerous continuous variables have distribution closely resemble the normal distribution.
The normal distribution can be used to approximate various discrete prob. dist.
The normal distribution provides the basis for classical statistical inference.
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13. Properties of Normal Distribution
It is symmetrical with mean, median and mode are equal.
It is bell shaped
Its interquartile range is equal to 1.33 std deviations.
It has an infinite range.
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Abdull Halim Abdul

14. Normal distribution is characterised by its mean, μ and its std deviation, σ.
And is denoted by N(μ , σ2)
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15. If a random variable X is distributed normal with the mean, μ and its std deviation, σ then
X ~ N(μ , σ2)
The probability distribution function of X is
*Page 250 (text book)
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Abdull Halim Abdul

16. Then P(X = a) = 0, where a is any constant.
If X ~ N(μ , σ2)
Then P(X = a) = 0, where a is any constant.
Previuosly it is very difficult to calculate the probability using the pdf. So all normal distribution is converted to std normal distribution, Z ~ N(0,1) for calculation.
i.e
Lecture 4
Abdull Halim Abdul

17. Using excel will be discussed using a few examples.
Calculation using std normal distribution table already discussed at school. It will only be discussed in the tutorial.
Using excel will be discussed using a few examples.
Lecture 4
Abdull Halim Abdul