Topic_ImportantProbabilityDistributions

Topic_ImportantProbabilityDistributions - ECON634...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
ECON634: Econometrics and Business Statistics Topic 4 Some Important Probability Distributions 1 ECON634 Shuping Shi
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Lecturer Lecturer: Dr Shuping Shi - Email: [email protected] - Phone: 9850 8501 - Office: Room 441, E4A Building - Monday: 12:00 2:00pm (W5C220) - Consultation: Monday 3:00-4:00pm during teaching weeks ECON634 Shuping Shi 2
Image of page 2
Probability Distributions Discrete probability distributions Binomial distribution Continuous probability distributions Normal distribution Chi-square distribution F-distribution T-distribution ECON634 Shuping Shi 3
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The Binomial Distribution A Bernoulli process has the following properties: There are two possible outcomes, which we call success and failure. The probability of a success is p , the probability of failure is (1- p ). If a fixed number, n , of Bernoulli trials are undertaken, the random variable representing the number of successes in the n trials has a binomial distribution . The trials are independent that is, the result of one trial does not affect the result of any other trials. ECON634 Shuping Shi 4
Image of page 4
The Binomial Distribution Use notation X~Bin(n,p) Examples: Flip a coin 10 times, X = number of heads. Then X is a binomial random variable, X~Bin(n,p) n=10, p=0.5 Do a survey of 1000 people, X = number of people who think current PM is doing a good job. X is a binomial random variable, n=1000, p=? ECON634 Shuping Shi 5
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Binomial Random Variable The number of successes in n trials, denoted by X. Possible values : 0, 1, 2, …, n Discrete random variable Formula to calculate probabilities: ECON634 Shuping Shi 6 x n x p 1 p ! x n ! x ! n x X P 1 2 ... 2 n 1 - n n n! : Note
Image of page 6
Example Example: A student sitting an econometric quiz decides to answer each of the 10 multiple choice questions entirely by chance. Each question has 5 options, only one of which is correct. Let X be the number of questions the student answers correctly. ECON634 Shuping Shi 7
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Is this a binominal experiment? conditions: There is a fixed finite number of trials ( n=10 ). An answer can be either correct or incorrect. Each answer is independent of the others. The probability of a correct answer (P(success)=.20) does not change from question to question. Then, X~Bin(n=10, p=0.2) ECON634 Shuping Shi 8
Image of page 8
What is the probability the student gets no answers correct? ECON634 Shuping Shi 9 dp) 5 (to 10737 . 0 8 . 0 1 1 2 . 0 1 2 . 0 ! 0 10 ! 0 ! 10 0 X P 10 0 10 0 x n x p 1 p ! x n ! x ! n x X P
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
What is the probability that the student passes (i.e. gets 5 or more correct)? ECON634 Shuping Shi 10 calculate! to formulas of lot a 10 X P 9 X P 8 X P 7 X P 6 X P 5 X P 5 X P
Image of page 10