Probability Density Function

#probability #interview

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, $\int_{[a, b]} p (x) d x$

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

What are the conditions of Probability Density Function?

The domain of P needs to have all the possible states/region of the random variable
$\forall x p (x) ⩾ 0$
$\int p (x) d x = 1$

References

Deep Learning by Ian Goodfellow

Related Notes

Likelihood
Negative Log Likelihood
Continuous Random Variable
Probability vs. Likelihood
Maximum Likelihood