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20 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Binomial Coefficient (Formula)
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The number of ways of arranging k successes among n observations
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Binomial Probability (Formula)
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Binomial Mean (Formula)
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Binomial Standard Deviation (Formula)
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Geometric Probability (Formula)
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Geometric Mean (Formula)
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Geometric Standard Deviation (Formula)
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Geometric Probability of the Success greater than a number of Trials (Formula)
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Geometric Setting
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1. Each observation falls into one of just 2 categories: success or failure.
2. The observations are all independent. 3. The probability of a success, p, is the same for each observation. 4. The variable of interest is the number of trials required to obtain the first success. |
Ex.
Flip a coin until you observe a tail. |
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Binomial Setting
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1. Each observation falls into one of just 2 categories: success or failure.
2. There is a fixed number n of observations. 3. The n observations are all independent. That is, knowing the result of one observation tells you nothing about the other observations. 4. The probability of a success, p, is the same for each observation. |
Ex.
When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random dialing machine makes 15 calls. X is the number that reach a live person. |
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Binomial Random Variable
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The random variable X = (number of successes) in a binomial setting.
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To do so, one must calculate the probability that P(x=k) for all values n through k. These probabilities should sum to a value close to one, in order to encompass the entire sample space.
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Binomial Distribution
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The distribution of the count X of successes in a binomial setting. n = the number of observations, p = the probability of success on any one observation, X = the whole numbers from 0 to "n".
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B(n,p)
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Probability Distribution Function (PDF)
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Function that assigns a probability to each value of X when given a discrete random variable X.
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Cumulative Binomial Function (CDF)
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Function that calculates the sum of the probabilities for 0, 1, 2, . . . , up to the value X when given a random variable X. It finds the probability of obtaining at most X successes in "n" trials.
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Binomial pdf
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Given a discrete random variable X, the probability distribution function (pdf) assigns a probability to each value of X.
Use: 2nd VARS, A |
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Binomial cdf
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Given a random variable X, the cumulative distribution function (cdf) of X calculates the sum of the probabilities for 0,1,2..., up to the value X. That is, it calculates the probability of obtaining at most X successes in n trials.
Use: 2nd VARS, B |
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P(X>n)
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P(X>n) = (1-p)^n
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Normal Approximation
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Use when np ≥ 10 and n(1-p)≥10
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2 conditions
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Factorial n! = ?
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n!= n*(n-1)*(n-2)*........*3*2*1
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Probability Distribution Function (pdf)
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Given a discrete random variable X, pdf assigned a probability of each value of X.
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