A function whose value at any given sample in the sample space can be explained as providing a relative likelihood that the value of the random variable would be equal to that sample is called a probability density function (PDF). It gives the probability that any value in a continuous set of values might occur. Its magnitude gives an idea of the likelihood of finding a continuous random variable near a certain point. A function defined on the outcomes of some probabilistic experiment which takes values in a continuous set is termed as a continuous random variable. These describe outcomes in probabilistic situations where the possible values some quantity can take form a continuum. In this article, we will discuss how to find the probability density function of a continuous random variable.
We can find PDF using the formula
If the random variable can be any real number, then PDF is normalized such that
The probability that X takes value between -∞ to +∞ is 1.
The non-normalized probability density function of a certain continuous random variable X is F(x) = 1/(1+x2). Find the probability that X is greater than 1, P(X>1)
The probability density function should be normalized.
The normalized Probability density function is