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.
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...
__________________________________
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
___________________________________
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...
__________________________________
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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[@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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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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[@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

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

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

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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.

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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

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[@user-rc3kr6rp2j]

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

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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.

[@openknect3386]

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

[@shashankbshivakumar4831]

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

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What about the CDF and PDF for normal distribution?

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[@tanya.24]

5:22 , how did you get this value?