PMF

What is a PMF?

In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete density function.

Histogram vs. PMF

A histogram is always calculated using a finite number of samples, while the pmf is what would be obtained with an infinite number of samples.

I do not know why the second line is not right. Instead they do not need much the solution is below.

I figured out the 3rd line easily with the hint. I try my best not to take the hint!