18. Probability

Question 1

Complementary Rule of Probability P.328

Answer 1

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

Question 2

Addition Rule of Probability P. 328

Answer 2

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

If A and B intersect, subtract the overlap area

Question 3

Contingency Table P.331

Answer 3

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

Question 4

Conditional Probability P.333

Answer 4

The probability of B occurring give that A has occurred.

P(B|A) = P(A∩B) / P(A); P(A) not 0

Question 5

Independent and Dependent Events P.334

Answer 5

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

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

Question 6

Mutually Exclusive Events P.335

Answer 6

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

Question 7

Multiplication Rule of Probabilities P.335

Answer 7

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)

Question 8

Permutations P.338

Answer 8

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

Question 9

Combination P.338

Answer 9

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

Question 10

Normal Distribution P.342

Answer 10

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

Question 11

Poisson Distribution P.347

Answer 11

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.

Question 12

Binomial Distribution P.348

Answer 12

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

Question 13

Chi Square Distribution P.350

Answer 13

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

Question 14

t-Distribution P.352

Answer 14

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

Question 15

F-Distribution P.354

Answer 15

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)

Question 16

Hypergeometric Distribution P.355

Answer 16

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

Question 17

Bivariate Normal Distribution P.357

Answer 17

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

Question 18

Exponential Distribution P.359

Answer 18

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

Question 19

Lognormal Distribution P.360

Answer 19

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.

Question 20

Weibull Distribution P.361

Answer 20

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)