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| What is a Random Variable |
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Definition
A variable, usually x, that has a single numerical value, determined by chance, for each outcome of a procedure. Two types: discrete and continuous |
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Term
| What is a Probability Distribution |
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Definition
a description that gives the probability for each value of the random variable. It is often in the form of a table, graph, or formula. |
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| What is a Discrete Random Variable |
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Definition
A discrete random variable is one which may take on only a countable number of distinct values such as 0, 1, 2, 3, 4, ... ex: number of children in a household, cinema attendance, ... |
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| What is a Continuous Random Variable |
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Definition
A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements ex: height, weight, amount of sugar in an orange, time required to run a mile.. |
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Term
What does the following stand for? ΣP(x) = 1 |
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Definition
| The sum of all probabilities must be 1 (where x assumes all possible values) |
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Term
What does the following stand for? 0 ‹ P(x) ‹ 1 |
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Definition
| each prob. value must be between 0 and 1 inclusive (for every individual value of x) |
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Term
| What is the standard deviation formula for 5-2? |
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Definition
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Term
| Standard Deviation Range Rule of Thumb |
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Definition
maximum usual value = μ + 2σ minimum usual value = μ - 2σ |
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Term
| What is the Rare Event Rule? |
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Definition
| If , under a given assumption, the prob. of a particular observed event is extremely small, we conclude that the assumption is probably not correct. |
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Term
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Definition
The expected value of a discrete random variable represents the average value of the outcomes. It is denoted as E. E = Σ[x * P(x)]
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Term
| Binomial Prob. Distribution |
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Definition
1. Fixed number of trials 2. Trials must be independent 3. Outcomes catergorized in 2 ways 4. Prob. of a success remains the same in all trials |
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Term
| What do S, F, p, q, n, x, and P(x) stand for? |
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Definition
S= success F= failure p= prob. of success in one of the n trials q= prob. of failure in one of the n trials n= fixed number of trials x=specific umber of successes in n trials, so x can be any whole number between 0 and 1, inclusive. P(x)= the prob. of getting exactly x successes amoung the n trials |
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Definition
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| What does P(F) = 1-p = q mean? |
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Definition
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Term
Are the following formulas for any Discrete Prob. Distribution or Binomial Distributions? μ = Σ[x*P(x)] σ2 = Σ[x2 * P(x)] - μ2 σ = √Σ[x2*P(x)] - μ2 |
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Definition
| Discrete Prob. Distribution |
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Term
Are the following formulas used for Discrete Prob. Distributions or Binomial Distributions? μ = np σ2 = npq σ = √npq |
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Definition
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Term
| What is the Poisson Distribution? |
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Definition
Discrete prob. distribution that applies to occurrences of some event over a specified interval of time, distance, area, volume, or some similar unit. |
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Term
| What are the variables and formula for Poisson Distribution? |
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Definition
x is the number of occurrences of the event in an interval. P(x) = μx * e-μ/ x! where e = 2.71828 |
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Term
| What are the four requirements for the Poisson Distribution? |
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Definition
1. the random variable x is the number of occurrences of an event over some interval 2.the occurrences must be random 3. the occurrences must be independent of each other 4. the occurrences must be uniformly distributed over the interval being used. |
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| What are the parameters of the Poisson Distribution? |
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Definition
the mean is μ the standard deviation is σ = √μ |
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