Family history

I don't know why, but I've been thinking about genetics, and where our genes come from. I'm no scientist, but I arrived at the following conclusion by simple deduction.
Males inherit the Y chromosome from the father via his father, and his father and so on. We get the X chromosome from the mother, her mother, her mother and so on.
Females inherit one X chromosome from the father, his mother, her mother, her mother and so on. The other X chromosome is inherited in the same way as for males.
I wonder if I'm right.