# stat400lec10 - Statistics 400 Lecture 10 Section 3.3 3.4...

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Statistics 400 Lecture 10 Section 3.3, 3.4 Expected value and Bernoulli Trials Review: Bernoulli Experiment: A Bernoulli experiment is a random experiment, the outcome of which can be classified as success and failure. Let X be random variable of Bernoulli distribution . Outcome Success 1 Failure 0 Probability p q=1-p Notation: X ~ Ber (p) Expected value E[X]=p Variance Var[X]=pq A sequence of Bernoulli Trials: A sequence of Bernoulli experiments are conducted independently and the probability of success (p) remains the same. Example: For a million of instant lottery tickets, suppose that 20% are winners, If 5 tickets are purchased, (1) what is the probability we have (0,1,0,1,0)? Ping Ma Lecture 10 Fall 2005 - 1 -

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(2) what is the probability we have (0,0,1,1,0)? (3) What is the probability we have two winning tickets? Binomial distribution 1. A Bernoulli experiment is performed n times 2. The trials are independent 3. The probability of success on each trial is a constant p; The probability of failure on each trial is a constant 1-p 4. The random variable X equals the number of successes in the n trials.

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