Bernoulli Trials

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Bernoulli Trials

• Two Possible Outcomes
• Success, with probability p
• Failure, with probability q 1 ? p
• Trials are independent.

2
Binomial Distribution

• For n Bernoulli trials, the number of successes X
  is a binomial random variable. The probability of
  k successes is given by the binomial probability
  formula
• As k varies with fixed n and p, the binomial
  probabilities define a binomial probability
  distribution over 0, 1, 2, , n.

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Mean and Standard Deviation of a Binomial RV

• Mean
• Standard Deviation

5
Law of Large Numbers

• Informal If n is large, the proportion of
  successes in n Bernoulli trials will be very
  close to p.
• Formal For Bernoulli trials with n and p, as n ?
  ?,for all ? gt 0, where k is the number of
  successes in the n trials.

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