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    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. $\int p(x) dx = 1$

    References