Applications of Probability Density Function

What is Probability Density Function?

Probability Density Function is used for calculating the probabilities for continuous random variables. When the cumulative distribution function (CDF) is differentiated we get the probability density function (PDF). Both functions are used to represent the probability distribution of a continuous random variable....

Probability Density Function Example

Let X be a continuous random variable and the probability density function pdf is given by f(x) = x – 1 , 0 < x ≤ 5. We have to find P (1 < x ≤ 2). To find the probability P (1 < x ≤ 2) we integrate the pdf f(x) = x – 1 with the limits 1 and 2. This results in the probability P (1 < x ≤ 2) = 0.5...

Probability Density Function Formula

Let Y be a continuous random variable and F(y) be the cumulative distribution function (CDF) of Y. Then, the probability density function (PDF) f(y) of Y is obtained by differentiating the CDF of Y....

How to Find Probability from Probability Density Function

To find the probability from the probability density function we have to follow some steps....

Graph for Probability Density Function

If X is continuous random variable and f(x) be the probability density function. The probability for the random variable is given by area under the pdf curve. The graph of PDF looks like bell curve, with the probability of X given by area below the curve. The following graph gives the probability for X lying between interval a and b....

Probability Density Function Properties

Let f(x) be the probability density function for continuous random variable x. Following are some probability density function properties:...

Mean of Probability Density Function

The mean of the probability density function refers to the average value of the random variable. The mean is also called as expected value or expectation. It is denoted by μ or E[X] where, X is random variable....

Median of Probability Density Function

The median is the value which divides the probability density function graph into two equal halves. If x = M is the median then, area under curve from -∞ to M and area under curve from M to ∞ are equal which gives the median value = 1/2....

Variance Probability Density Function

The variance of probability density function refers to the squared deviation from the mean of a random variable. It is denoted by Var(X) where, X is random variable....

Standard Deviation of Probability Density Function

The standard deviation is the square root of the variance. It is denoted by σ and is given by:...

Probability Density Function Vs Cumulative Distribution Function

The key differences between Probability Density Function (PDF) and Cumulative Distribution Function (CDF) are listed in the following table:...

Types of Probability Density Function

There are different types of probability density functions given below:...

Probability Density Function for Uniform Distribution

The uniform distribution is the distribution whose probability for equally likely events lies between a specified range. It is also called as rectangular distribution. The distribution is written as U(a, b) where, a is the minimum value and b is the maximum value....

Probability Density Function for Binomial Distribution

The binomial distribution is the distribution which has two parameters: n and p where, n is the total number of trials and p is the probability of success....

Joint Probability Density Function

The joint probability density function is the density function that is defined for the probability distribution for two or more random variables. It is denoted as f(x, y) = Probability [(X = x) and (Y = y)] where x and y are the possible values of random variable X and Y. We can get joint PDF by differentiating joint CDF. The joint PDF must be positive and integrate to 1 over the domain....

Applications of Probability Density Function

Some of the applications of Probability Density function are:...

Solved Examples on Probability Density Function

Problem 1: If the probability density function is given as: [Tex]\bold{f(x)= \begin{cases} x / 2 & 0\leq x < 4\\ 0 & x\geq4 \end{cases}} [/Tex] . Find P (1 ≤ X ≤ 2)....

Probability Density Function – FAQs

What is a Probability Density Function (PDF)?...