Discrete Probability Distributions l Chapter 5 l Discrete Probability Distributions 5.1 Binomial Probability Distribution 5.2 Poisson Probability Distribution

5.1 Binomial Probability Distribution An experiment in which satisfied the following characteristic is called a binomial experiment: The random experiment consists of n identical trials. Each trial can result in one of two outcomes, which we denote by success, S or failure, F. The trials are independent. The probability of success is constant from trial to trial, we denote the probability of success by p and the probability of failure is equal to (1-p) = q.

5.1 Binomial Probability Distribution Examples: No. of getting a head in tossing a coin 10 times. No. of getting a six in tossing 7 dice. A firm bidding for contracts will either get a contract or not

5.1 Binomial Probability Distribution A binomial experiment consist of n identical trial with probability of success, p in each trial. The probability of x success in n trials is given by If X~ B(n, p), then

5.1 Binomial Probability Distribution Given that X~B (12, 0.4), find Answer: 0.0639 0.1419 0.2128 0.4185 4.8 2.88

5.1 Binomial Probability Distribution Cumulative Binomial Distribution

5.1 Binomial Probability Distribution Given X~B (25, 0.15), using tables of Binomial probabilities, find Answer: 0.8385 0.6821 0.0255 0.3099 0.7442 0.3178

5.1 Binomial Probability Distribution

5.2 Poisson Probability Distribution A random variable X has a Poisson distribution and it is referred to as a Poisson random variable if and only if its probability distribution is given by (Lambda) is the long run mean number of events for the specific time or space dimension of interest. A random variable X having a Poisson distribution can also be written as with

5.2 Poisson Probability 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. Examples: 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.

5.2 Poisson Probability Distribution Given that , find Answer: 0.0082 0.0307 0.9918

5.2 Poisson Probability Distribution Suppose that the number of errors in a piece of software has a Poisson distribution with parameter . Find The probability that a piece of software has no errors. The probability that there are three or more errors in piece of software . The mean and variance in the number of errors. Answer: 0.05 0.577 ?

5.2 Poisson Probability Distribution The no. of points scored by Team A in 1 basketball match is Poisson distributed with mean 2.4. What is the probability that the team scores at least 16 points in 4 matches Answer: 0.0362