Cumulative Distribution Functions and Probability Density Functions

This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or normal distribution. The cumulative distribution function or cdf allows you to calculate the area under the curve to the left of some point of interest in order to evaluate the accumulated probability.
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Statistics - Video Lessons:
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Introduction to Probability:
• Introduction to Probab...
Probability Formulas:
• Probability Formulas, ...
Probability Explained:
• Probability Explained!
Probability With Geometry:
• Probability With Geome...
Probability of Complementary Events:
• Probability of Complem...
Conditional Probability:
• Conditional Probabilit...
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Independent and Dependent Events:
• Probability - Independ...
Probability of Mutual Exclusive Events:
• Probability of Mutuall...
Multiplication and Addition Rule:
• Multiplication & Addit...
Compound Probability:
• Compound Probability o...
Expected Value:
• How To Calculate Expec...
Probability Tree Diagrams:
• Probability Tree Diagrams
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Bayes Theorem:
• Bayes' Theorem of Prob...
Probability - Binomial Distribution:
• Finding The Probabilit...
Probability - Geometric Distribution:
• Geometric Distribution...
Probability - Poisson Distribution:
• Introduction to Poisso...
Continuous Probability Distributions:
• Continuous Probability...
Probability Density Functions:
• Cumulative Distributio...
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Probability - Uniform Distributions:
• Continuous Probability...
Probability - Exponential Distributions:
• Probability Exponentia...
Probability - Normal Distributions (Calculus):
• Normal Distribution & ...
Probability - Standard Normal Distributions:
• Standard Normal Distri...
Probability - The Law of Large Numbers:
• Law of Large Numbers
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Final Exams and Video Playlists:
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[@TheOrganicChemistryTutor]

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Thank you!! This is such a clear explanation. I am taking a grad class way over my head and my dissertation research is using surveys and we keep talking about PDFs and CDF and I have been so lost. So clear to me now, thanks bunches!

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[@lightningllama]

"Area under the curve at that point to the left" One line that cleared all my doubts. Thank you

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This video makes cumulative distribution functions and probability density functions easier for me.

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[@yaweli2968]

It’s true that the CDF for the uniform is (x-a)/(b-a) but if the entire area is not up to one, for instance, if b is the 70th percentile instead of the 100th, this implies the entire area adds up to 70 percent. The CDF changes. It’s the everything like before multiplied by 0.7. Props to this Professor, he is amazing for all courses, what else can this man not teach!

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[@siddiqisah1452]

The Area of line technically referes to an infintesimally area under the curve being a trapizium out the whole distribution equal to one.You can use the leibenz calculus theorem for that.

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Great explanations!

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[@Syko1985]

i would have liked an explanation to why the CDF of a exponential is 1-e^(-(lambda)x)

[@m.b.9026]

It's because that's the integral from 0 to x. Which is the area under a function

[@WAYN3SCHL3G3L]

I find it very interesting that you don't even mention integrals once. What made you choose to do it that way?

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[@marijatosic217]

Where did the lambda go in 5:33 ? Why do we calculate 1 - e^-lambda * x? Shouldn't it be 1 - lambda*e^lambda*x, since that is our f(x)? Thank you :)

[@alexssandredeoliveiraj2773]

To evaluate the area under the curve to the left of some value "x", you have to calculate the integral of f(x) between 0 and x. Doing this the lambda will vanish.

[@charithmenaka7399]

really helpful

[@shashankbshivakumar4831]

How can f(x) = 1((b-a) when there is no x in the function?

[@abdorabie7032]

Thank you

[@asbinanceasbinance1473]

Thanx a lot!

[@미기엘라이]

Why did he omit a lambda on a expression of exponential distribution, when he obtain a CDF of exponential distribution?

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[@openknect3386]

Well, it does explain why CDF is the integration of of PDF.

[@armelkarate9684]

Very good video. However you should have shown why the cdf for an exponential distribution is 1-exp(-lx) instead of putting the formular. I encourage students to avoid memorization. This can be shown through an integral and you know it but you didn't do it.

[@ultimateassasins63]

Using this video for learning as I'm currently taking a probability course in college and I'm thinking the same thing. Wish he explained the CDF for exponential.

[@MA-yu6wb]

Pdf tell you the shape of graph. Cdf tell you the left area of some value

[@davedeatherage4902]

Excellent!

[@haneulkim4902]

@9:16 So to find area between a,b we just integrate pdf from b to a?

[@jh-gp1cm]

Thank you :)

[@roseytb4092]

Hi How do I calculate p when I have chi-square?

[@MrGelare]

I am looking for bases that support the reasons why we do not add or subtract CDF. I wonder if anyone could help me find the rule

[@50LOT1]

what about the normal dis ?

[@donjr3270]

Wait, did you explain the normal distribution part?

[@alexzheng982]

What about the CDF and PDF for normal distribution?

[@haneulkim4902]

What is area under CDF represent? I've tried it with exponential pdf, cdf with lambda 1 and integral of cdf seems to give me pdf.