Constant random variable

Question

How do I plot the cumulative distribution function and probability mass function of the constant random variable $X(\omega)=2$ for all $\omega$?

Answer 1

If $P(X = c) = 1,$ then that equation is all that's necessary to show the PMF.

The CDF $F_X(x)$ is $0$ for $x < c$ and $1$ for $x \ge c.$

Here is a plot of the CDF for the case $c = 3.$

Answer 2

The CDF is: $$P(X\leq x) = \begin{cases} 1 \quad \text{ if } x \geq 2 \\ 0 \quad \text{ if } x < 2 \\ \end{cases}$$

while the PMF is: $$P(X = x) = \begin{cases} 1 \quad \text{ if } x = 2 \\ 0 \quad \text{ if } x \not= 2 \\ \end{cases}$$