$1.$ Create three vectors. County consists the name of ten counties in California. Population consists their population. Income consists their median household income. Create a data frame including those three variables. Provide the R code only.

$2.$ Last year, each family received a tax credit of $$1000.$ Calculate the adjusted income for the ten counties using one R command. Provide the R code only.

$3.$ Calculate the mean, median, maximum, minimum, variance, standard deviation, first quartile, and third quartile of the population. Provide both the R code and the result.