Continuous Probability Distributions - Basic Introduction

This statistics video tutorial provides a basic introduction into continuous probability distributions. It discusses the normal distribution, uniform distribution, and the exponential distribution. The probability is equal to the area under the curve and the total area under the curve is equal to 1. This video gives you some formulas that you might find helpful. It also briefly discusses the difference between continuous random variables and discrete random variables.
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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[@TheOrganicChemistryTutor]

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A great tutorial for the topic.

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Surprised you didn't sneak in the standard deviation of the exponential distribution is equal to the mean of the distribution.

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What is mean formula in exponential distribution

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[@preciousmaelane274]

Why do we divide the standard deviation of a uniform distribution with square root of 12??

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[@vigneshwarvijayaraj9689]

Uniform distribution is a type of discrete distribution right? Correct me if I am wrong

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Yes correct, there’s a continuous one and a discrete uniform distribution

[@roberte.6892]

W/ respect to the exponential distribution, what is "e"?

[@dialglex]

"e" is Euler's number, which is a mathematical constant approximately equal to 2.71828

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7:52 why 12? for when we are finding the standard deviation

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[@TheCivilizedCaveman]

but how do you calculate the area under the curve??? 2:08

[@matthewthompson6455]

Integral baby

[@TruthNerds]

(Unsurprisingly,) you only cover absolutely continuous distributions. The other principal type of continuous distribution, singular distributions, is not even mentioned. To be honest, they are a mathematical curiosity and I've only heard of them myself today. 😄 But now it appears to me that starting with continuous distributions in general first, i.e. the distribution function, and then going from there to absolutely continuous distributions (such that the derivative is the probability density function) arguably makes more sense didactically than starting with the density function and using integral calculus to then explain distribution functions. For instance, if you start with the distribution function F(x), then P(x ∈ [a,b]) = F(b) - F(a), which is simpler (and more general) than the integral approach (area under the curve).

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