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Lecture Notes Chapter 3

# Lecture Notes Chapter 3 - .Ifweletp heads,then(1p) ontails....

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Consider the toss of a single weighted coin.   Suppose a 0 is recorder if the result is tails and a  1 is recorded if the result is heads.  If we let p  denote the probability that the coin lands on  heads, then (1-p) is the probability that it will land  on tails.  What is the probability distribution for this  experiment? x p(x) 0 1-p 1 p total 1

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By looking at the table, you can give a simple  formula for p(x): p(x)=p x (1-p) 1-x . Thus p(0) = 1 – p, and p(1) = p. We call such a distribution a  Bernoulli  Distribution . A Bernoulli distribution is a single experiment  which has two possible outcomes, a success and  a failure. The probability of success will be denoted by p,  and the probability of failure is 1-p.
Let X have a Bernoulli Distribution, what is E(X)  and V(X)? Fill out the table: So E(X) = p and V(X) = p - p 2  = p( 1 – p ).

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Lecture Notes Chapter 3 - .Ifweletp heads,then(1p) ontails....

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