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Binomial distribution_mfcs module 5ppt.pptx
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- 2. Random Variable Types ofRandom Variable • Discrete Random Variable • Continuous Random Variable Types of Probability Distributions Discrete Probability Distributions Continuous Probability Distributions
- 3. Probability Distributions • DiscreteProbability Distributions – Poisson distribution, – Bernoulli distribution, – Binomial distribution, – Geometric distribution, – Negative binomial distribution, – Multinomial binomial distribution, – Categorical distribution • Continuous Probability Distributions – Normal distribution, – Gaussian distribution, – Exponential distribution
- 4. Types of Probability Distributions DiscreteProbability Distributions Continuous Probability Distributions Binomial Probability Distribution Normal Probability Distribution Poisson Probability Distribution Exponential Probability Distribution
- 5. BINOMIAL DISTRIBUTION Jacob Bernoulli(also known as James or Jacques) (1654 – 1705)
- 6. Binomial Distribution • Bimeans two. When only two outcomes are possible, binomial distribution is prepared – example – throw of coins – (Head or tail) trials are independent p= probability of success q= probability of failure • Binomial distribution was discovered by James Bernoulli in 1738. • It is also known as Bernoulli Distribution or Bernoulli Theorem. • This theorem was published eight years after the death of James Bernoulli in 1713. • Finite number of trials – with exclusive and exhaustive outcomes • This is a discrete probability distribution.
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- 9. Binomial Distribution • Adiscrete probability distribution (applicable to the scenarios where the set of possible outcomes is discrete, such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a probability mass function. • If ‘X’ is a discrete random variable with probability mass function (r=x) Where X= 0, 1, 2, 3, ….., n and q = 1 – p , then ‘X’ is a binomial variate and the distribution of ‘X’ is called binomial distribution.
- 10. N=0 1 N=1 11 N=2 1 2 1 N=3 1 3 3 1 N=0 0C0 =1 N=1 1C0 = 1 1C1=1 N=2 nCr 2 C0 = 1 2 C1 =2 2 C2 =1 N=3 3C0 =1 3C1 = 3 3C2 = 3 3C3 = 1 N=4 4C0 = 1 4C1= 4 4C2= 6 4C3 = 4 4C4 =1
- 11. Binomial Distribution • Theword “binomial” literally means “two numbers”. A binomial distribution for a random variable X (known as binomial variate) is one in which there are only two possible outcomes, success and failure, for a finite number of trials. • We define success and failure, the two events must be mutually exclusive and complementary; that is they cannot occur at the same time and the sum of their probability is 1 (i.e. 100%)
- 12. Binomial Distribution Examples • Ifyou are purchasing a lottery then either you are going to win money or you are not. In other words, anywhere the outcome could be a success or a failure that can be proved through binomial distribution. • If someone tosses the coin then there is an equal chance of outcome it can be heads or tails. There is a 50% chance of the outcomes. • Examples of election polls; whether the party ‘A’ will win or the party ‘B’ will win in the upcoming election. Whether by implementing a certain policy the government will get the expected results within a specific period or not. • If you are appearing in an exam then there is also an equal possibility of getting passed or fail.
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- 14. Examples Example- 5.1 Example- 5.2 Example-5.3 Example- 5.4
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