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Statistics
Discrete Probability Distributions
16
Mathematics
Undergraduate 1
10/28/2011

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Term
Probability Distributions
Definition
Describe what will probably happen(for each value of a variable determined by chance) instead of what actually did happen, and are often given in the format of a graph, table or formula
Term
Random Variable
Definition
A variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure (or experiment)
Term
Discrete Random Variable
Definition
Either a finite number of values or countable number of values where "countable" refers to the fact that there might be infinitely many values, but they result from a counting process. EX; number of people in a pool..
Term
Continuous Random Variable
Definition
Infinitely many values, and those values can be associated with measurements on a scale without gaps or interruptions. EX; the speed of a car..
Term
Requirements for a Probability Distribution
Definition
∑P(x) = 1
where x assumes all possible values
and
0 ≤ P(x) ≤ 1
for every individual value of x
Term
(Formula)
Probability Distribution Mean
Definition
μ = ∑ [x P(x)]
can be done on calculator by entering data in lists, then using STAT CALC 1-Var Stats L1,L2 ENTER; x bar is the mean
Term
(Formula)
Probability Distribution Standard Deviation
Definition
σ = √∑ [ (x - μ)² • P(x)]
can be done on calculator by entering data in lists, then using STAT CALC 1-Var Stat L1,L2; σx is the standard deviation
Term
(Formula)
Probability Distribution Variance
Definition
σ²=∑ [ (x - μ)² • P(x)]
Term
Range Rule of Thumb
Definition
Most values should lie within 2 standard deviations of the mean. We can therefore identify the "unusual" values by determining if they lie outside these limits;
maximum usual value = μ + 2σ
minimum usual value = μ - 2σ
Term
Using Probabilities to Determine When Results are Unusual
Definition
-Unusually high if P(x or more) ≤ .05
-Unusually low if P(x or fewer) ≤ .05
Term
Binomial Probability Distribution
Definition
A procedure that meets all of the following requirements;
1. Has a fixed number of trials
2. Trials mush be independent
3. Each trial must have all outcomes classified into 2 categories (success, failure)
4. Probability of success remains the same in all trials
Term
Notations for Binomial Probability Distributions
Definition
p denotes probability of success
q denotes probability of failure; 1-p=q
n denotes fixed number of trials
x number of successes in n trials
Term
(Formula)
Binomial Probability Distribution Mean
Definition
μ = n • p
Term
(Formula)
Binomial Probability Distribution Standard Deviation
Definition
σ = √npq
Term
(Formula)
Binomial Probability Distribution Variance
Definition
σ²
Term
(Calculator)
Given a Binomial Probability Distribution, what function do you use to find the probability of exactly x successes among a trial?
Definition
binompdf(n,p,x)
2nd VARS, arrow up, select binompdf(
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