R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this [1]:

\[ \begin{equation} \begin{aligned} \operatorname{cov}(X, Y) &=\mathrm{E}[(X-\mathrm{E}[X])(Y-\mathrm{E}[Y])] \\ &=\mathrm{E}[X Y-X \mathrm{E}[Y]-\mathrm{E}[X] Y+\mathrm{E}[X] \mathrm{E}[Y]] \\ &=\mathrm{E}[X Y]-\mathrm{E}[X] \mathrm{E}[Y]-\mathrm{E}[X] \mathrm{E}[Y]+\mathrm{E}[X] \mathrm{E}[Y] \\ &=\mathrm{E}[X Y]-\mathrm{E}[X] \mathrm{E}[Y] \end{aligned} \end{equation} \] \[ \begin{equation} \begin{array}{|c|c|c|c|c||c|} \hline & \multicolumn{3}{|c||}{\boldsymbol{x}} & \multicolumn{1}{c|}{f_Y(y)} \\ \cline { 1 - 5 } f(x, y) & \multicolumn{1}{|c|}{5} & 6 & 7 & \\ \hline \boldsymbol{y} & \mathbf{8} & 0 & 0.4 & 0.1 & 0.5 \\ \hline & 9 & 0.3 & 0 & 0.2 & 0.5 \\ \hline f_X(x) & 0.3 & 0.4 & 0.3 & 1 \\ \hline \end{array} \end{equation} \]

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

[1]
A. Y. Chaudhari and P. Mulay, “Cloud4NFICA-nearness factor-based incremental clustering algorithm using microsoft azure for the analysis of intelligent meter data,” in Research anthology on smart grid and microgrid development, IGI Global, 2022, pp. 423–442.
[2]
M. J. Crawley, Statistics: An introduction using r. John Wiley & Sons, 2014.
[3]
A. Field, J. Miles, and Z. Field, “Discovering statistics using r.” Sage London, 2012.
[4]
V. Egoshin, S. Ivanov, N. Savvina, G. Z. Kapanova, A. Grjibovski, et al., “Descriptive statistics using r.” Ekologiya Cheloveka/Human Ecology, no. 9, pp. 55–64, 2018.