# Ch 5.3

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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
 Author: khonka ID: 46334 Card Set: Ch 5.3 Updated: 2010-11-01 01:37:56 Tags: Statistics Folders: Description: Binomial Distribution Show Answers: