05ProbDist

05ProbDist - Statistical Techniques I EXST7005 Probability...

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Statistical Techniques I EXST7005 Probability distributions You are here
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Probability PROBABILITY - a measure of the likelihood of the occurrence of some event An event can be any outcome (e.g. verbal, mathematical, graphical)
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If the event is certain to occur, the probability is (one, unity). P(A) = 1 If the event is certain to NOT occur, the probability is 0 (zero, null) P(A) = 0 The probability of an event will always range be between 0 and 1 (inclusive) 0 P(A) 1 Some rules of Probability
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Some rules of Probability (continued) The sum of the probability of all possible events where the events are mutually exclusive, is 1. Where the events are Ai, for i=1,2,. ..,r Σ P(Ai)=1 Special note for truly continuous variables. The probability of a given number for a truly continuous variable is zero (0).
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The Binomial Distribution First example of a distribution A binomial distribution consists of a set of binomial observations or Bernoulli trials, these are observations with two possible, mutually exclusive, outcomes. Examples Have you taken EXST7005? Yes, No A given fish is: Male, Female A given fish is: Tagged, Untagged A coin toss is: Heads, Tails
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The Binomial Distribution (continued) Our first experiment, toss three coins Possible outcomes are Coin 1 Coin 2 Coin 3 Frequency of heads Tail Tail Tail 0 Tail Tail Head 1 Tail Head Tail 1 Head Tail Tail 1 Tail Head Head 2 Head Tail Head 2 Head Head Tail 2
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(continued) Number of Heads frequency (f) relative frequency (r.f.) Probability 0 1 1/8 P(0)=0.125 1 3 3/8 P(1)=0.375 2 3 3/8 P(2)=0.375 3 1 1/8 P(3)=0.125 Total 8 1 1 Note that each event is equally likely and mutually exclusive. Prepare a frequency table of the results.
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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05ProbDist - Statistical Techniques I EXST7005 Probability...

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