,

,

Rather

,

,

ingredients

forestry

σ2^pσp^2\sigma^2_{\hat{p}} which

result

, recall,

nnn the

, depending on the size of the sampling fraction

fact it’s

(11.15) and

SRSWR the

N1/N1/N, then

Then

, as we’ll see in Section 11.3.4,

, notice,

, expressed as a percent,

population and

NNN at

population and, hence,

,

SRS this

,

,

, for one small example population,

So

μ\mu,

, with variance σ2¯yQ=σy¯Q2=\sigma^2_{\bar{y}_Q}= 4.38,

,

among

,

,

among

,

)

11.2 the

,

,

,

) then

respectively.

letters and

be:

sample size

, or all possible samples,

, but equally valid,

estimate but

estimator which

,

So,

unit we

unit and

Here

10.1 where

, but unknown,

) and

selection and

, in this context,

Therefore

practice this

, and the majority of the material in this book,

(2019) who

,

Like the mean() and median() functions we saw previously,

ha, then

then

,

,

then

Now

then

at and around

,

,

,

histogram shown

A closed interval, denoted by square brackets, means the endpoints are included in the interval. For example, [50,150][50,150][50, 150] in Table 11.1 is a closed interval with endpoints 50 and 150. There are 7 population units with biomass (Mg/ha) that fall within this interval. A closed interval can also be written using ≤≤\le notation, e.g., [50,150]={50≤y≤150}[50,150]={50≤y≤150}[50, 150]=\{50 \le y \le 150\}. An open interval, denoted by parentheses, means the endpoints are not included in the interval. Following from open and closed notation, a half-open interval includes only one of its endpoints, and is denoted by one parentheses and one square bracket, e.g., there are 8 units that fall within the half-open interval (150,250](150,250](150,250] or {150<y≤250}{150<y≤250}\{150 < y \le 250\}.

and selected

,

,

, but large,

tables and

,

Similarly, yiyiy_i=1 if the iii-th individual is diseased and yiyiy_i=0 otherwise.

means then

Often

,

,

“average” we’re

population and

,

??

,

R and,

:

for:

task and

,

Also

, in fact

,

,

, with its default behavior,

vectors

, in addition to printing the data frame’s dimensions (i.e., number of rows and columns),

With its ever expanding functionality, documentation, and user community,

, in Section 1.2.1,

is

,

cases it

extreme it’

ggplot() followed

EDA

Hopefully

) and

,

So

) and

So,

Also

fact all

,

) hence

aesthetic use

example we’re

??

i.e.

then

,

units which

then

2 njnjn_j

1 n

So,

data. We’ll

Now

So

,

operator and

and

,

,

truncated and

,

vector, then

elementwise

elementwise

x you

,

,

For example n∑i=1xiyi=x1y1+x2y2+…+xnyn,(10.8)(10.8)∑i=1nxiyi=x1y1+x2y2+…+xnyn,\begin{equation} \sum^n_{i=1}x_iy_i = x_1y_1 + x_2y_2 + \ldots + x_ny_n, \tag{10.8} \end{equation} which, following PEMDAS, we recognize multiplication of xixix_i and yiyiy_i should come before the summation.

then

, recall,

then

,

Now

then

Here

,

encounter

,

,

,

,

,

,

, within the jjj-th plot,

kkk and

data and index

2j=2j=2 there

measured and

1j=1j=1 there

plot and

now let’s

often we

Similarly, for example, when i=2i=2i = 2 then xixix_i equals 1, when i=3i=3i = 3 then xixix_i equals 5, and so on.

,

1 and

2 there

,

)y=(1,4,5)y=(1,4,5) which

) or

,

case the

??

then

,

,

is:

So,

statistics which

characteristic and

,

,

cases we’re

, as covered in this book,

, found in publications and reference material,