 Hello and welcome to the session. In this session, we will discuss probability density function. Now if a random variable, capital X takes the value x1, x2 and so on up to xn with the probabilities p of x1, p of x2 and so on up to p of xn respectively, x1 plus p of x2 plus xn is equal to 1 is greater than or equal to 0 for the function p is called the function of a random variable capital X and is set to define the probability distribution of the random variable capital X. Now where the random variable considered are discrete, that is, the random variable capital X can take at most a countable finite number of values. For example, the random variable capital X will be equal to 0, 1, 2, the probability density function of a continuous random variable capital X. Now let be a continuous function of a random variable capital X, f of x dx given X, that is the random variable capital X falls in the infinitesimal interval, that is, which is greater than the probability density function of a random variable capital X, y is equal to 2 so defined is known as the probability density function that is simply the density function of a random variable is usually abbreviated Df, that is, the probability density function of a random variable capital X. Now the probability in the interval of length dx, the probability A to B will have the random variable capital and less than equal to B is equal to the integral from A to X. The properties of the probability density function of a random variable capital X is equal to 0 where X is greater than minus infinity random variable is taken to be the open interval minus infinity to infinity by taking the value of the function f to be 0. We write x is equal to 0, x is less than A, f of x is equal to greater than equal to A and less than equal to B equal to 0, that is, we are taking the value of the function f to be 0. This when x is less than A, then f of x is equal to 0 and when x is greater than B, then also f of x is taken as integral from minus dx is equal to 1. Then the upper random variable capital X which is greater than equal to B is equal to integral that satisfies these conditions can be taken to be the probability density function of a random variable capital X. So in this session we have learnt about probability density function and this completes our session. Hope you all have enjoyed the session.