Business Statistics (BQT 173) ІМ ќ INSTITUT MATEMATIK K E J U R U T E R A A N U N I M A P Discrete Probability Distribution: Binomial Distribution
Binomial Distribution Binomial distribution is the probability distribution of the number of successes in n trials. E.g. 1. No. of getting a head in tossing a coin 10 times. 2. No. of getting a six in tossing 7 dice. 3. No of missile hits the target. Lecture 4Abdull Halim Abdul2
Binomial distribution is characterised by 1. the number of trial, n and 2. the probability of success in each trial, p And is denoted by B(n,p) Lecture 4Abdull Halim Abdul3
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) = n C x p x (1-p) n-x *Page 221 (text book) *in text book π is used instead of p Lecture 4Abdull Halim Abdul4
Example If X~B(4,0.1) then P(X=3) = 4 C 3 (0.1) 3 (0.9) 1 = P(X=4) = 4 C 4 (0.1) 4 (0.9) 0 = 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 4Abdull Halim Abdul5
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. examples Lecture 4Abdull Halim Abdul6
Business Statistics (BQT 173) ІМ ќ INSTITUT MATEMATIK K E J U R U T E R A A N U N I M A P Discrete Probability Distribution: Poisson Distribution
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. 1. No. of cars passing a toll booth in one hour. 2. No. defects in a square meter of fabric 3. No. of network error experienced in a day. Lecture 4Abdull Halim Abdul8
Poisson distribution is characterised by the mean success, λ. And is denoted by P o (λ) Lecture 4Abdull Halim Abdul9
If a random variable X is distributed Poisson with the parameter λ then X ~ P o (λ) The probability distribution of X is *Page 228 (text book) Lecture 4Abdull Halim Abdul10
Example If X~ P o (3) then P(X=2) = = 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 4Abdull Halim Abdul11
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. examples. Lecture 4Abdull Halim Abdul12
Business Statistics (BQT 173) ІМ ќ INSTITUT MATEMATIK K E J U R U T E R A A N U N I M A P Continuous Probability Distribution: Normal Distribution
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. Lecture 4Abdull Halim Abdul14
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. Lecture 4Abdull Halim Abdul15
Normal distribution is characterised by its mean, μ and its std deviation, σ. And is denoted by N(μ, σ 2 ) Lecture 4Abdull Halim Abdul16
If a random variable X is distributed normal with the mean, μ and its std deviation, σ then X ~ N(μ, σ 2 ) The probability distribution function of X is *Page 250 (text book) Lecture 4Abdull Halim Abdul17
If X ~ N(μ, σ 2 ) 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 4Abdull Halim Abdul18
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. examples Lecture 4Abdull Halim Abdul19