PDF vs. CDF: Difference Between PDF and CDF

# PDF vs. CDF: Difference Between PDF and CDF

clickHere
Vikram Singh
Assistant Manager - Content
Updated on Feb 9, 2024 12:33 IST

Pdf describes the probability distribution of a continuous random variable, while cdf describes the probability distribution of both discrete and continuous random variables. In this article, we will learn the difference between pdf and cdf.

The probability distribution of a random variable is a list of all possible outcomes with corresponding probability values, and different functions are used to describe this probability distribution. Probability Density Function and Cumulative Distribution Function are among such functions.

The probability Density Function describes the probability distribution of continuous random variables. Cumulative Distribution Function is a probability distribution that deals with continuous and discrete random variables.

In this article, we will learn the difference between PDF and PDF in probability.

Must Explore – Statistics for Data Science Online Courses

Before starting the article, let’s discuss random variables.

A Random Variable is a numerical description of the outcome of a random experiment. Generally, it is represented by X.

It is of two types:

Discrete Random Variable: It has a countable number of values between two values.

Continuous Random Variable: It has an infinite number of values between two values.

Example: Distance Travelled

Now, let’s start with the probability density function vs cumulative distribution function based on the different parameters.

## CDF vs PDF: Difference Between PDF and CDF

Difference between Variance and Standard Deviation
Variance and Standard Deviation are statistical measure to measure the dispersion of data point from the center or mean. In this article, we will discuss difference between variance and standard...read more
Nominal vs. Ordinal
There are four levels of measurements: Nominal, Ordinal, Interval and Ratio. Nominal and Ordinal are qualitative data, whereas Interval and Ratio are quantitative data. In this article, we will discuss...read more
Difference between One-tailed and Two-Tailed Test
One-tailed and two-tailed test are statistical hypothesis tests to accept or reject the null hypothesis. In this article, we will briefly discuss the difference between one tail and two tail...read more

## What is the Probability Density Function

PDF (or Probability Density Function) is a function that describes the probability of a continuous random variable. The PDF function’s curve looks like a bell-shaped curve, and it takes the value between the given intervals.

• It tells the probability that a random variable takes on a certain value.

Your Career Awaits: Discover the Best Government Job-Oriented Courses After 10 & Online Government Certification Opportunities

### Formulas

The Probability density function of a continuous random variable X is a function fX: R -> [0, inf) such that:

Where R is a real number.

Standard Error vs. Standard Deviation
Standard Error quantifies the variability between sample drawn from the same population, whereas the standard deviation quantifies the variability of values in a dataset. In this article we will discuss...read more
Difference between Median and Average
Average and median are two basic terms that are used in statistics very often. Median is the middle value in a set, whereas average is an arithmetic mean of set...read more
Correlation vs Causation
Correlation and causation are one of the most important but confusing topics of statistics. Correlation gives the relationship between two variables, whereas causation means one event is cause due to...read more

### Properties

• The value of PDF is always greater than or equal to 1.
• The area under the PDF curve is always equal to 1.
• The median divides the PDF curve into two equal halves.
Difference between Accuracy and Precision
Precision refers to the closeness of multiple reading of the same quantity, whereas accuracy refers to the measured value to the true value. In this article we will discuss difference...read more
Sensitivity vs. Specificity: What’s the Difference?
Sensitivity and Specificity are often used interchangeably, but they are two different concepts. Sensitivity refers to the ability of a test to identify those with the disease correctly. In contrast,...read more
ROC-AUC vs Accuracy: Which Metric Is More Important?
ROC-AUC and Accuracy are the important metrices that are used to evaluate the machine learning model performance. In this article, we will discuss the difference between the ROC-AUC and Accuracy.

### Example

If

f(x) = x, if 0 < x < 1

f(x) = 2 – x, if 1 < x < 2 and

f(x) = 0, otherwise

Then, f(x) is a probability density function centred at x = 1.

## What is the Cumulative Distribution Function?

CDF or Cumulative Distribution Function is a probability that a random variable takes on a value less than or equal to X. The CDF can be defined. for both the random variables: continuous and discrete random variables.

### Formula

The CDF (Cumulative Distribution Function) of a random variable X is defined as

FX(X) = P (X <= X),

for all x in R.

Continuous Variable: How it is Different from Discrete Variable
A numerical variable is said to be a continuous variable if it can take an infinite number of real values within a given interval or range. This article will discuss...read more
Difference Between Probability and Non Probability Sampling
The main difference between probability and non-probability sampling is that probability sampling gives every member of the population an equal chance of being selected, while non-probability sampling does not. Learn...read more
Difference Between Population And Sample
The article discusses the concept of population and sample in statistics and the difference between population and sample.

### Properties

• CDF is a non-decreasing.
• The minimum of CDF is 0 when x = – infinity: Fx(- inf) = 0.
• The maximum of CDF is 1 when x = infinity: Fx(inf) = 1
• P [a <= x <= b] = FX(b) – FX(a)

### Example

Consider the pdf function given in the above example and find the CDF for ½ <= x <= 3/2.

## Relation Between PDF and CDF

• CDF can be found using PDF by simply integrating PDF.
• PDF can be obtained using CDF by differentiating CDF.

## What are the key differences between PDF and CDF?

1. PDF is the probability that a random variable will take a value exactly equal to the random variable. In contrast, CDF is the probability that a random variable will take a value less than or equal to the random variable.
2. PDF applies only for continuous random variables, while CDF applies for continuous and discrete random variables.
3. The value of CDF is always non-negative, whereas the value of PDF lies between 0 and 1.
Top 10 Probability Questions Asked in Interviews
Probability is defined as the likeliness of something to occur or happen. In this article, we will discuss top 10 probability questions that are asked in the interviews with their...read more
Probability Density Function: Definition, Properties, and Application
Probability Density function describes the probability distribution of the continuous random variable. In this article, we will briefly discuss what is probability density function, its properties, its application, and how...read more
Introduction to Maximum Likelihood Estimation: Definition, Type and Calculation
Maximum Likelihood Estimation is used to estimate the parameter value of the likelihood function. This article will briefly discuss the definition, types and calculation of MLE.

## Conclusion

In this article, we have discussed the probability density function (PDF) and cumulative density function (CDF), their properties and the difference between CDF and PDF with the help of examples.

PDF (or Probability Density Function) is a function that describes the probability of a continuous random variable. The PDF function’s curve looks like a bell-shaped curve, taking the value between the given intervals. In contrast, CDF or Cumulative Distribution Function is a probability that a random variable takes on a value less than or equal to X. The CDF can be defined. for both the random variables: continuous and discrete random variables.

Hope you will like the article.

Keep Learning!!

Keep Sharing!!

Difference Between List and Set
In this article, we will briefly cover what lists and sets are in Java and Python, the difference between them, and the features of lists and sets.
Difference Between Bit and Byte
A bit is the most basic unit of information in computing and digital communication, represented as 0 and 1, while a byte consists of eight bits. In this article, we...read more
Difference Between Algorithm and Pseudocode
An algorithm is a step-by-step procedure for performing a task or solving a problem, whereas pseudocode is an end-to-end description of an algorithm in formal English (or in natural language)...read more
Difference Between HTML and CSS
In this article, we will discuss what is html, what is CSS and the difference between them with the help of example. Later in the article we will also discuss...read more
Difference Between Web Browser and Web Server
In this article, we will briefly discuss what Web Browser and Web Servers are, their features, and the differences between them.
Difference Between Public and Private Sector
At some point, we all must have heard the terms Public and Private sectors. But only a few of us know the difference between public and private sector. If you...read more

## FAQs on Difference Between

What is PDF?

PDF (or Probability Density Function) is a function that describes the probability of a continuous random variable. The PDF function's curve looks like a bell-shaped curve, and it takes the value between the given intervals.

What is CDF?

CDF (or Cumulative Distribution Function) is a probability that a random variable takes on a value less than or equal to X. The CDF can be defined. for both the random variables: continuous and discrete random variables.

What is the difference between PDF and CDF?

A PDF, or Probability Density Function, shows the likelihood of a continuous random variable assuming specific values. In contrast, a CDF, or Cumulative Distribution Function, represents the probability that the variable is less than or equal to a particular value. The PDF is used more for continuous variables, while the CDF can be applied to both continuous and discrete variables.

When to use PDF and CDF?

PDF is mainly used in statistical analysis and modeling to describe the distribution of data, whereas CDF are commonly used in statistical analysis and modeling to calculate probabilities and percentiles.

Can a PDF convert to a CDF?

Yes, PDF can be converted to a CDF by integrating the PDF over its entire domain. The resulting function will be the CDF of the random variable and vice versa.

How do PDF and CDF function for discrete random variables?

For discrete random variables, the PDF (in this case, more accurately referred to as a Probability Mass Function or PMF) outlines the probabilities for each specific value. The CDF accumulates these probabilities, showing the cumulative probability for values up to and including a specific point.

Can you calculate probabilities using both PDF and CDF?

Yes, both can be used to calculate probabilities, but in different ways. For continuous random variables, the PDF can find cumulative probabilities over a range, whereas the CDF gives the cumulative probability up to a specific value.