Flashcards in 18. Probability Deck (20)

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1

## Complementary Rule of Probability P.328

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

2

## Addition Rule of Probability P. 328

###
P(A or B) = P(A) + P(B)

If A and B intersect, subtract the overlap area

3

## Contingency Table P.331

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

4

## 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

5

## Independent and Dependent Events P.334

###
Independent

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

Dependent

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

6

## 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.

7

## 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)

8

## 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

9

## 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

10

## Normal Distribution P.342

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

11

## 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.

12

## 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

13

## Chi Square Distribution P.350

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

14

## t-Distribution P.352

###
Used when n<30, or population SDV is unknown for normal distribution.

DF= n-1

15

## 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)

16

## 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

17

## Bivariate Normal Distribution P.357

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

18

## Exponential Distribution P.359

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

19

## 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.

20