Unit 5 Data Quick Memorize Formulas
This deck covers key probability distributions, including hypergeometric, normal approximation, geometric, binomial, and uniform distributions, along with their formulas and conditions.
When do we use hypergeometric and what formulas do we use?
The hypergeometric distribution is one unlike any of the others. There are 3 conditions which must be fulfilled:
Trials that are not identical
Trials that are dependent
Two possible outcomes; success or failure
Hypergeometric distribution probability formula
P(x) = (aCx)(n-aCr-x)/nCr
where n = # of possible outcomes
a = # of successful outcomes r = # of dependent trials
x = number of required successes
Hypergeometric distribution expected value = probability of success times the number of dependent trials.
E(x) = r (a/n)
Key Terms
When do we use hypergeometric and what formulas do we use?
The hypergeometric distribution is one unlike any of the others. There are 3 conditions which must be fulfilled:
Tria...
P(x) = (aCx)(n-aCr-x)/nCr
E(x) = r (a/n)
Trials that are not identical
Trials that are dependent
Two possible outcomes; success or failure
hypergeometric distribution
Normal approximation
Standard deviation can be calculated by 𝜎=√(npq)
Condition for normal approximation = ...
𝜎=√(npq)
np>5 and nq>5
normal approximation
geometric distributions
Wait time
Example: Determine the probability of producing 3 cars before finding a defec...
P(x) = (q^x) (p)
E(x) = q/p
Wait time
geometric distributions
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| Term | Definition |
|---|---|
When do we use hypergeometric and what formulas do we use? | The hypergeometric distribution is one unlike any of the others. There are 3 conditions which must be fulfilled: Hypergeometric distribution probability formula P(x) = (aCx)(n-aCr-x)/nCr where n = # of possible outcomes Hypergeometric distribution expected value = probability of success times the number of dependent trials. E(x) = r (a/n) |
P(x) = (aCx)(n-aCr-x)/nCr E(x) = r (a/n) Trials that are not identical Trials that are dependent Two possible outcomes; success or failure | hypergeometric distribution |
Normal approximation | Standard deviation can be calculated by 𝜎=√(npq) Condition for normal approximation = If X is a binomial random variable of n independent trials, each with probability of success p, and if np>5 and nq>5. This lets the binomial random variable be approximated by a normal distribution. |
𝜎=√(npq) np>5 and nq>5 | normal approximation |
geometric distributions | Wait time Example: Determine the probability of producing 3 cars before finding a defect if the probability of a defect is 1%. The formula for geometric distribution probability is: P(x) = (q^x) (p) Expected value |
P(x) = (q^x) (p) | geometric distributions |
Binomial distributions | P(x) = nCx (p^x) (q^n-x) n = # of trials p = probability of successes x = # of successes q = probability of failure E(x) = np where n = number of trials and p = probability of success Bernoulli Trials, they consist of: Are the trials identical? Trials have to be done the same way each time. Are the trials independent? The first outcome of a trial does not impact the next. Do the trials have two outcomes (success or failure)? The desired outcome will either happen (success) or not happen (failure) |
P(x) = nCx (px) (q n-x) n = # of trials p = probability of successes x = # of successes q = probability of failure E(x) = np where n = number of trials and p = probability of success Bernoulli Trials, they consist of: | Binomial distribution |
Uniform distribution | When all outcomes in a distribution are equally likely in any single trial, we call this a uniform probability distribution. Expected value - an expectation/expected value, E(X), is the predicted average of all possible outcomes in a single trial of a probability experiment. Expected value is the long-run average. Formula E(X) = sum of x P(x) |
P(X) = 1/n | uniform distribution |