A global variable in R is a variable that is defined outside of any function and can be accessed from anywhere in the program. It is stored in the global environment and is accessible to all functions and code segments within the R session. Global variables can hold data or configuration settings that need to be accessed and modified across multiple functions or code blocks.

The sqrt() function in R is used to calculate the square root of a number. For example, sqrt(4) would return 2.

To calculate a running median in R, you can use the rollapply() function from the zoo package. The rollapply() function allows you to specify a window size and apply a function (such as median()) to a rolling window of values. This can be useful for analyzing time series or other sequential data.

The strsplit() function in R is used to split a string into components based on a specific character or string. For example, strsplit("Hello World", " ") would return a list with two components: "Hello" and "World".

The legend() function in R can be used to add a legend to a plot. It allows you to specify the labels and colors corresponding to different elements in the plot, making it easier to interpret the plot.

In R, if a variable is not found in the local environment of a function, the function will look in the parent environment. This allows functions to access variables defined in higher-level environments, such as variables defined outside the function but within the parent environment.

The ifelse() function in R has the syntax ifelse(condition, value_if_true, value_if_false). It evaluates the condition and returns the value_if_true if the condition is true, and the value_if_false if the condition is false. This function allows for vectorized conditional operations.

R stores all data in RAM, and as such, it might struggle with large datasets. This can sometimes limit its speed and efficiency, particularly in a data-intensive environment. However, there are packages and strategies to manage and overcome this limitation.

The primary use case for nested functions in R is to encapsulate helper functions within a larger function. Nested functions can help in reducing code duplication, improving code modularity, and organizing related functionality together. They are especially useful when implementing complex algorithms or workflows that require multiple steps or subroutines.

In R, "==" is a comparison operator used to test for equality, while "=" is used for assignment, especially in the context of function arguments. However, "<-" is more commonly used for assignment.