Ch 5.3
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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(k1)..2x1...
 0! = 1

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

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

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

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) p^{x}(1p)^{nx }or nCx p^{x }q^{nx} wher q=1p

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)

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