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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
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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
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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
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Binomial distribution
- is the probability distribution for the number of successes in a sequence of Bernoulli trials
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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
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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)
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Mean and standar deviation for binomial variable with parameters n adn p are
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