Probability Density Function

[!def] Probability Density Function
For defining the probability for the continuous variables, we use the probability density function.

Rather than giving the direct probability for a random variable, it gives the probability of a value to be in an infinitesimal region. We can find out the actual probability by integrating on the region range.

So to find out if the value x is in the range $[a, b]$, we can find out that by, $\int_{[a, b]} p(x) dx$

Like, Probability Mass Function to be a probability density function there are some conditions need to be satisfied,

[!question] What are the conditions of Probability Density Function?

  1. The domain of P needs to have all the possible states/region of the random variable
  2. $\forall x : p(x) \geqslant 0$
  3. $\int p(x) dx = 1$