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.
How To Find PDF 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.
Example
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).
Solution:
The probability density function should be normalized.
The normalized Probability density function is
= 1/4
Related Links:
Cumulative Frequency Distribution
Frequently Asked Questions
What do you mean by Probability Distribution in probability theory?
A mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment is a probability distribution.
What do you mean by Probability Density Function?
A function that defines the relationship between a random variable and its probability, so that we can find the probability of the variable using the function, is called a Probability Density Function (PDF).
What do you mean by Continuous Random Variable?
A random variable X is continuous if possible values contain either a single interval on the number line or a union of disjoint intervals.
Give the formula to find the PDF of a continuous random variable.
The formula to find PDF of a continuous random variable is given by P(a≤ X ≤ b) = ∫ab f(x) dx.
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