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Flashcards in 18. Probability Deck (20):

Complementary Rule of Probability P.328

P(A) = 1 - P(not A)


Addition Rule of Probability P. 328

P(A or B) = P(A) + P(B)
If A and B intersect, subtract the overlap area


Contingency Table P.331

Contingency tables provide an effective way of arranging attribute data while allowing us to readily determine relevant probabilities.


Conditional Probability P.333

The probability of B occurring give that A has occurred.
P(B|A) = P(A∩B) / P(A); P(A) not 0


Independent and Dependent Events P.334

P(A|B) = P (A) or vise versa

P(A|B) not P(A) or vise versa


Mutually Exclusive Events P.335

Two events A and B are said to be mutually exclusive if both event cannot occur at the same time.


Multiplication Rule of Probabilities P.335

If Independent
P(A∩B) = P(A) x P(B)

If Dependent
P(A∩B) = P(A) x P(B|A)
P(A∩B) = P(B) x P(A|B)


Permutations P.338

Arrangement of a set of objects with regard to the orders of the arrangement.

P(n,r) = nPr = n! /(n-r)!
Permutation of n objects taken r at a time


Combination P.338

Selection of objects without regard to the order in which hey are selected.

C(n,r) = nCr = nPr /r! = n! /r!(n-r)!
Combination of n objects taken r at a time


Normal Distribution P.342

Bell curve normal distribution with Mean=0 and SDV.=1


Poisson Distribution P.347

The number of rare events (defect) that will occur during a specific period or in a specific area or volume (per unit).

The mean (expected) number of events and variance are both denoted by Greek letter lambda.


Binomial Distribution P.348

P(X) = n! /x!(n-x)! P^X (1-P)^n-x

n! /x!(n-x)! = Number of ways x success in n trails (nCr)
P^X (1-P)^n-x = Probability of obtaining x success in n trials


Chi Square Distribution P.350

Used to find a confidence interval for Population Variance. (like distribution for Population Mean)


t-Distribution P.352

Used when n<30, or population SDV is unknown for normal distribution.
DF= n-1


F-Distribution P.354

Comparing two population variances. If X and Y are two random variables distributed as X^2 with v1 and v2 degrees of freedom, then the random variable is distributed as F-Distribution with DF v1= n-1 in the numerator and DF v2 =n-2 in the denominator.

F = (X/v1) / (Y/v2)


Hypergeometric Distribution P.355

The experiment consists of randomly drawing n elements without replacement from a set of N elements, r of which are S's (success) and (N - R) of which re F's (failure)

Hypergeometric random variable x is the number of S's in the draw of n elements.

Hypergeometric = Dependent
Binomial = Independent


Bivariate Normal Distribution P.357

Joint probability density function of two dependent random variables (normal distributed).


Exponential Distribution P.359

The length of time or the distance between occurrence of random events (wait time distribution).


Lognormal Distribution P.360

Continuous probability distribution of a random variable whose logarithm is normally distributed. This distribution has applications in modeling life spans for products that degrade over time.


Weibull Distribution P.361

A specialized form of the gamma distribution and is highly useful in the area of reliability.
Although the Weibull distribution is actually a three-parameter distribution, it is sometimes referred as two-parameter because the location parameter is assumed to be zero. (Scale, Shape, Location Parameters)