Consider the following schema of a DataFrame (named packages_DF) created in PySpark:

root |-- date: date (nullable = true)

|-- time: string (nullable = true)

|-- size: integer (nullable = true)

|-- r_version: string (nullable = true)

|-- r_arch: string (nullable = true)

|-- OS: string (nullable = true)

|-- package: string (nullable = true)

|-- version: string (nullable = true)

|-- country: string (nullable = true)

|-- ip_id: string (nullable = true)

The schema represents a log file of downloads of R packages from the CRAN mirror. Write code to answer the following questions:

Use PySparks DataFrame functions to show total number of counts by each IP. Use PySparks DataFrame functions to show top 5 highest number of downloads count by country. Use PySparks SQL to show total downloads by each OS. Use PySparks SQL to show average size of each package. Use PySparks SQL to show highest download date for package dplyr.