Suppose we toss a coin which is not fair. and the probability of success is 0.7. Is that enough to decide on the shape of it beta distribution ? what would be its shape then ?
As far as I know, it's the probability of success that we map in the X-axis. so, it should be between 0 and 1. But in some articles and books I've found, x axis has some values beyond that. I'm confused.
pls help
A random variable is a mapping from random outcomes of any sort into the number line. For a categorical random variable, the categorical outcomes are mapped to numeric outcomes such as 0 for failure, 1 for success. Probability distributions are then a mathematical description of the relative likelihood of a random variable's different values. They are usually expressed in terms of the set of possible outcomes along the X-axis, and either the corresponding probability or density (for discrete or continuous, respectively) along the Y-axis.
Why do you think a coin toss should have a beta distribution? The beta distribution is a continuous distribution, meaning there are an infinite number of possible outcomes it can have. Your coin toss can only have two possible outcomes, heads or tails. That's described by a classic Bernoulli random variable with p = 0.7 for "success" and, implicitly, q = 1-p = 0.3 for failure.
