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Binomial Distribution

Binomial Distribution. A binomial experiment possesses the following properties 1 – a fixed number, n, of trials 2 – two outcomes for each trial 3 – constant probability of ‘success’ on each trial 4 – independence between any two trials . Binomial Random Variable.

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Binomial Distribution

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  1. Binomial Distribution A binomial experiment possesses the following properties • 1 – a fixed number, n, of trials • 2 – two outcomes for each trial • 3 – constant probability of ‘success’ on each trial • 4 – independence between any two trials

  2. Binomial Random Variable • A discrete random variable that counts the number of successes on n trials of a binomial experiment is said to be a binomial random variable.

  3. Examples of binomial random variables: • The number of spark plugs that fail when a car engine is ignited • The number of heads in twenty tosses of a fair coin • The number of ‘sevens’ in three rolls of a pair of dice • The number of defective items in a quality sample of 25

  4. Binomial Mass Function • x P[X=x] • 0 p0(1-p)n • 1 n*p1(1-p)n-1 • . • . • . • n pn(1-p)0

  5. Plots of binomial probabilities

  6. Plots n=20

  7. Plots n = 100

  8. Expected value and variance of a binomial random variable • E[B] = n*p • V[B] = n*p*(1-p)

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