Ch 5.3

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Author:
khonka
ID:
46334
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Ch 5.3
Updated:
2010-10-31 21:37:56
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Statistics
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Binomial Distribution
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  1. Factorals
    • Trial - each reptition, particularly the experiment (each trial) has only two possible outcomes. ex. testing the effectiveness of a drug: for each patient the drug is either effective or not effective ( 2 possible outcomes)
    • k! = k(k-1)..2x1...
    • 0! = 1


  2. Binomial Coefficients
    • if n is a positive integer and x is a nonnegative integer less than or equal to n, then the binomial coefficient (n )is defined as

  3. Bernoulli Trials
    • are repeated trials of an experiment, if the following 3 conditions are statisfied:
    • 1. the experiment (each trial) has two possible outcomes, denoted generically s, for success, and f, for failure
    • 2. the trials are independet
    • 3. The probability of a success, called the success probability and denoted p, remains the same from trial to trial

  4. Binomial distribution
    • is the probability distribution for the number of successes in a sequence of Bernoulli trials


  5. To find a Binomial Probability Formula


    • Assumptions
    • 1. n trials are to be performed
    • 2. Two outcomes, success or failure, are possible for each trial
    • 3. The trials are independent
    • 4 The success probability, p, remains the same from trial to trial
    • Step 1. Identify a success,
    • Step 2. Determine p, the success probability
    • Step 3. Determine n, the number of trials
    • Step. 4 The binomial probability formula for the number of successes, X, is given by
    • P(X=x) = (n/x) px(1-p)n-x or nCx px qn-x wher q=1-p


  6. Cumulative probability


    • < uses less then or equal
    • P(X<x) the concept of concept of probability applies to any random variable
    • Between two specified number - say, a and b in term of cumulative probability
    • P(a<X<b) = P(X<b) - P(X<a)

  7. Mean and standar deviation for binomial variable with parameters n adn p are

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