# What does $p$ represent in the CDF of a mixed distribution?

" Some random variables are mixtures of a discrete random variable and a continuous random variable. They have CDF of the form $$F_X=pF_{X_1}+(1-p)F_{X_2}$$ where $$0\lt p \lt 1$$ and $$F_{X_1}$$ is the CDF of a discrete random variable

and $$F_{X_{2}}$$ is the CDF of a continuous random variable.

I've read that p (and 1-p) are mixture weights but what exactly are these mixture weights?

It looks like p is the probability that X is discrete and 1-p is the probability that X is continuous? Is this interpretation correct?

Flip a weighted coin with probability $$p$$ of heads. If the coin comes up heads, draw $$X$$ from distribution $$1$$, if it comes up tails, draw it from distribution $$2$$. This describes how you would generate a variable from this distribution if you can generate variables from the two parent distributions.