Histogram of binomial distribution~rbinom(1000,100,0.3)

set.seed(10)
binomial_data <- rbinom(1000,100,0.3)
binomial_data <- as.data.frame(binomial_data)
names(binomial_data) <- c("data")
#This code sets the seed for reproducibility and generates 1000 samples from a binomial distribution with n=100 and p=0.3

library(tidyverse)

## -- Attaching core tidyverse packages ------------------------ tidyverse 2.0.0 --
## v dplyr     1.1.0     v readr     2.1.4
## v forcats   1.0.0     v stringr   1.5.0
## v ggplot2   3.4.1     v tibble    3.2.1
## v lubridate 1.9.2     v tidyr     1.3.0
## v purrr     1.0.1     
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
## i Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

binomial_data %>% ggplot()+ geom_histogram(aes(x=data, y= stat(count/sum(count))), color="black")+
  geom_vline(xintercept = 30, size=1, linetype="dashed", color="red")+
  theme_bw()+ labs(x="Number of successes in 100 trials", y="proportion", title = "1000 samples of binom(100, 0.3")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

#NOTES:    Setting the Seed: The use of set.seed(10) ensures reproducibility. By setting the seed before generating random numbers, you guarantee that others can reproduce your results exactly. This is particularly important when sharing or collaborating on data analysis projects.

    #Data Generation: The rbinom(1000, 100, 0.3) function generates 1000 samples from a binomial distribution with parameters n=100n=100 (number of trials) and p=0.3p=0.3 (probability of success). These samples represent the number of successes in 100 trials and are stored in the binomial_data data frame.

    #Data Frame Conversion: Converting the vector of binomial data into a data frame (as.data.frame(binomial_data)) is optional but can be useful for compatibility with other data manipulation and visualization functions in R.

   #ggplot2 for Visualization: The ggplot2 package is used for creating the histogram and additional plot elements. The geom_histogram function is employed to generate the histogram, and the geom_vline function adds a vertical dashed line at x=30x=30, which could represent a critical threshold or point of interest.

    #Proportion on the Y-axis: The y = stat(count / sum(count)) aesthetic inside geom_histogram scales the y-axis to show proportions instead of counts. This helps in comparing distributions with different sample sizes.

   # Customization with theme_bw(): theme_bw() is applied to give the plot a clean black and white appearance. Themes in ggplot2 allow for easy customization of the plot's visual aspects.

    #Labels and Title: The labs function is used to add labels to the x-axis, y-axis, and title of the plot. Descriptive labels are essential for making the plot easily interpretable.

    #Knitting the Document: Knitting the R Markdown document converts the code and text into a dynamic document, incorporating the output of the code chunks. This makes it easy to share analyses, including both the code and its results.

    #Reproducibility and Collaboration: The combination of R Markdown and setting the seed ensures that your analysis is reproducible. Others can run your R Markdown document and obtain the same results. This is crucial for collaborative work and when sharing analyses with others.