You should begin with the definition of mean and variance, and also with finding $p(0)$ and $p(1)$.dylbester said:
A probability mass function is a mathematical function that describes the probability distribution of a discrete random variable. It assigns a probability to each possible outcome of the random variable.
A PMF is used for discrete random variables, whereas a PDF is used for continuous random variables. A PMF gives the exact probability of a specific outcome, while a PDF gives the probability density at a given point.
A PMF must satisfy two properties: 1) The probability assigned to each outcome must be between 0 and 1, and 2) The sum of all probabilities must equal 1.
A PMF can be used to calculate the probability of a specific outcome or a range of outcomes. This is done by summing the probabilities of all the outcomes within the desired range.
No, a PMF is only used for discrete random variables. For continuous random variables, a probability density function (PDF) is used to describe the probability distribution.
