Probability and Statistics

Question 1

probability

Answer 1

the measure of how likely a particular event or outcome is to occur

Question 2

statistics

Answer 2

the analysis and interpretation of numerical data

Question 3

factorial n!

Answer 3

• product of all positive integers from 1 to n
• for example
  6 ! = 6 x5x4 x3 x2x1= 720
  -equal to the number of ways of arranging n distinct objects in a sequence

Question 4

permutation

Answer 4

• an order-conscious subset of elements taken from a set
• order is significant –abc and bca are different permutations
  For example if a set contains a,b,c and d, 24 permutation of three elements are possible: abc, abd, acb, acd, adb, adc, bac, bad, bca, bcd, bda, bdc, cab, cad, cba, cbd, cda, cdb, dab, dac, dba, dbc, dca, dcb

Question 5

combination

Answer 5

• a subset of elements taken from a set
• order is not significant– abc and bca are the same combination
  For example, if a set constains a,b,c and d four combinations of three elements are possible: abc, abd, acd, and bcd
  The combination abc could also be written as acb, bac, bca, cab, or cba. All six represent the same combination

Question 6

set

Answer 6

a collection of elements

Question 7

elements

Answer 7

a single item or outcome

Question 8

outcome

Answer 8

a possible result of an experiment or trial

Question 9

event

Answer 9

A set of outcomes that satisfy a particular condition

Question 10

sample space, S

Answer 10

• the set containing all possible items or outcomes in the situation being studied
• also called universe, U

Question 11

independent events

Answer 11

• if the success or failure of event A has no affect on the probability of even B, then the two events are independent
  For example, a die is rolled twice:
• Event A is rolling a six on the first roll of a die
• Event B is rolling a six on the second roll
  Events A & B are independent

Question 12

dependent events

Answer 12

• If the success or failure of events A affects the probability of event B, then the two events are dependent

Question 13

mode

Answer 13

the value that occurs most frequently in the sample set

Question 14

median

Answer 14

the point in the sample set at which there are equal numbers of samples above and below

Question 15

mean

Answer 15

the sum of all samples in the set divided by the numbers of samples

Question 16

weighted arithmetic mean

Answer 16

• used when some data are more significant than others

- wi= weight assigned to datum, Xi

Question 17

geometric mean of the sample

Answer 17

• the number that, when raised to the power of the sample size, gives the product of all samples

Question 18

root mean square value

Answer 18

the square root of the arithmetic mean of the squares of all squares

Question 19

standard deviation

Answer 19

measures amount of dispersion in data set

• low means that data tend to be gathered close to mean value
• high means that data tend to be spread out over wide range of values

Question 20

variance

Answer 20

the square of the standard deviation

Question 21

random variable

Answer 21

assigns a real value to each possible sample point in sample space

Question 22

discrete random variables

Answer 22

there are finite numbers of possible numbers that the random variable can take on

Question 23

continuous random variables

Answer 23

• the random variable can take on any value over an interval on the real number line

Question 24

probability density function (PDF)

Answer 24

• Provides probability to each numerical output of the random variable (RV)
• In the case of continuous RV, the PDF gives the density at that point
• In the case of discrete RV, the PDF is a sum of impulses, each impulse with a magnitude of the probability equal to that numerical outcome

Question 25

binomial distribution

Answer 25

• Given n trials the binomial distribution provides the likelihood that there will x successes
• n is the number of trials
• p is the probability of success
• q is the probability of failure whre
  q=1-p

Question 26

normal or Gaussian distribution

Answer 26

• frequently occurring a natural distribution when multiple random parameters all effect the outcome

Question 27

unit normal table

Answer 27

• the probability density function, f(x) is difficult to evaluate
• instead, it is common to use a unit normal table to find values for the corresponding cumulative distribution function Fx(x)
• a unit normal table is normalized for a mean of zero and a standard deviation of one

Question 28

t-distribution

Answer 28

estimating statistics of normal distribution when sample size is small

• arises when using sample mean and variance as estimates for normal distribution
• student’s t-test used for testing significance of difference between two sample means
• as number of degrees of freedom increases, t-distribution approaches normal distribution

Question 29

hypothesis testing

Answer 29

the process of making decision with a specified level of confidence about a statistical parameter being evaluated

Question 30

common hypothesis tests

Answer 30

• Determine whether the average value taken from n samples could have come from a certain type of distribution
• Determine whether the sample variance taken from n sample could have come from a certain type of distribution

Question 31

null hypothesis H0

Answer 31

assumption being tested

Question 32

alternative Hypothesis, H1

Answer 32

must be true if H0 is not true