Chp2 Stats

Question 1

What is a random variable

Answer 1

It is a variable whose possible values are drawn from the outcome of a random phenomenonR

Question 2

Random variable examples

Answer 2

Tossing a coin, Tossing a die

Question 3

Two types of R.V.

Answer 3

Discrete, Continuous

Question 4

What do we assume about the observed data

Answer 4

It is a random sample where each sample is drawn from X where each xi is independently and identically distributed.

Question 5

Discrete

Answer 5

Takes on a countable number of possible values

Question 6

Continuous

Answer 6

Takes on an infinite number of possible values within a given range

Question 7

Probability Mass Function

Answer 7

For discrete variables,

Question 8

Probability Density Function

Answer 8

For continuous variables,

Question 9

Kernel density estimation

Answer 9

A statistical technique that smooths out data points

Question 10

Measures of central tendency

Answer 10

Mean
Median
Mode

Question 11

Mean

Answer 11

Average of all data points

Question 12

Robustness

Answer 12

The tendency to not be affected by extreme values

Question 13

Is the mean robust?

Answer 13

No

Question 14

How to obtain a robust mean

Answer 14

Trimmed mean, which occurs after extreme values on either side are discarded

Question 15

Median

Answer 15

The middle value when the data points are arranged in order

Question 16

Is the median robust?

Answer 16

Yes

Question 17

Mode

Answer 17

The most frequent occurring value in the dataset

Question 18

Is mode a useful measure of central tendency?

Answer 18

May not be

Question 19

When is robustness important?

Answer 19

When your data might contain anomalies or extreme values that could distort the overall analysis

Question 20

Measures of dispersion

Answer 20

Variance
Standard Deviation

Question 21

Variance

Answer 21

A measure of how much the values of X deviate from the expected (mean) value of X – measure of dispersion

Question 22

Sample standard deviation

Answer 22

The squared root of sample variance

Question 23

What does standard deviation tell you

Answer 23

It directly tells you how much, on average, each data point deviates from the mean – just makes number small

Question 24

bi-variate/multi-variate analysis

Answer 24

Can consider multiple vectors, as oppose to just 1 with varaince/std

Question 25

What does bi-variate analysis try to understand

Answer 25

The association or dependence on X1 and X2

Question 26

How to calculate mean and variance (first and second moment) in multivariate?

Answer 26

Same as normal, but return a vector instead of a single value

Question 27

How to get total variance for multivariates

Answer 27

Sum all individual variances in the output vector

Question 28

Covariance

Answer 28

Measure of the association or linear dependence between two variables

Question 29

How to summarize covariance information for n attributes

Answer 29

nxn covariance matrix

Question 30

Main diagonal of the matrix

Answer 30

Holds the variance of the column with itself

Question 31

Is covariance matrix symmetric?

Answer 31

Yes

Question 32

Correlation between two variable

Answer 32

The standardized covariance obtained by normalizing the covariance with the std of each variabl

Question 33

Which is dimensionless and which is in units obtained by multiplying the two variables

Answer 33

Correlation is dimensionless Covariance is in units obtained by multiplying the two variables

Question 34

Range of covariance

Answer 34

-inf, + inf

Question 35

Range of correlation

Answer 35

-1, 1

Question 36

what does correlation of 1 mean?

Answer 36

As one variable increases so does the other

Question 37

Collinearity

Answer 37

Occurs when the two variables are so highly correlated that we can use one to predict another ; one variable is a linear combination of the other variable

Question 38

Normal/Gaussian Distribution

Answer 38

Parameterized by mean and std mean = median = mode

Question 39

std decreases what happens to normal/gaussian distribution

Answer 39

Becomes steep and short

Question 40

Binomial distribution

Answer 40

Parameterized by n (number of trials) and p (probability of success in each trial) mean: np Median: [np] Variance: np(1-p)

Question 41

Power-law distribution

Answer 41

Long tailed distributions, Relationships where one quantity varies as a power of another Hard to define

Question 42

Power law distribution example

Answer 42

Area of square, quadruples when length is doubled

Question 43

Visualization is

Answer 43

Important

Question 44

XY plots

Answer 44

Scatter plots, birds eye view of how your data is distributed

Question 45

Boxplots

Answer 45

Whisker plots. Maximum, 3rd quartile, median, first quartile, minimum max and min are outliers

Question 46

Short rectangle in box plot means

Answer 46

data is similar

Question 47

Long whiskers

Answer 47

High std and variance

Question 48

Empirical cumulative distribution function

Answer 48

CDF(y) of a dataset X at a value y is the ration of samples that are lower that the value y.

Question 49

what is cdf (X,15) X= [2, 7, 8, 9, 10, 15, 16, 20]

Answer 49

CDF(X, 15) = 6/8 = 0.75

Question 50

CDF PDF relation

Answer 50

PDF is derivative of CDF